🕸Systems Engineering: Cellular Automata (Definitions)

"Cellular automata are mathematical models for complex natural systems containing large numbers of simple identical components with local interactions. They consist of a lattice of sites, each with a finite set of possible values. The value of the sites evolve synchronously in discrete time steps according to identical rules. The value of a particular site is determined by the previous values of a neighbourhood of sites around it." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"A mathematical construct and technique that models a system in discrete time and discrete space in which the state of a cell depends on transition rules and the states of neighboring cells." (Charles M Macal, "Agent Based Modeling and Artificial Life", 2009) 

[Cellular automaton:] A spatially-extended dynamical system in which spatially-discrete cells take on discrete values, and evolve according to a spatially-localized discrete-time update rule." (James E Hanson, "Emergent Phenomena in Cellular Automata", 2009)

"A spatiotemporal modeling technique in which a set of rules is applied to determine the state transitions of individual cells based on each cell’s current state and the states of its neighbors." (May Yuan, "Challenges and Critical Issues for Temporal GIS Research and Technologies", 2009) 

"Cellular Automata (CA) are discrete, spatially explicit extended dynamic systems composed of adjacent cells characterized by an internal state whose value belongs to a finite set. The updating of these states is made simultaneously according to a common local transition rule involving only a neighborhood of each cell." (Ramon Alonso-Sanz, "Cellular Automata with Memory", 2009) 

"Cellular automata are dynamical systems that are discrete in space, time, and value. A state of a cellular automaton is a spatial array of discrete cells, each containing a value chosen from a finite alphabet. The state space for a cellular automaton is the set of all such configurations." (Burton Voorhees, "Additive Cellular Automata", 2009) 

"They are dynamical systems that are continuous, local, parallel, synchronous and space and time uniform. Cellular automata are used to model phenomena where the space can be regularly partitioned and where the same rules are used everywhere [...]" (Jerome Durand-Lose, "Universality of Cellular Automata", 2009)

"A discrete model consisting of a grip of cells each of which have a finite number of defined states where the state of a cells is a function of the states of neighboring cells and the transition among states is according to some predefined updating rule. (Brian L Heath & Raymond R Hill, "Agent-Based Modeling: A Historical Perspective and a Review of Validation and Verification Efforts, 2010)

"A cellular automaton is composed of a set of discrete elements - the cells - connected with other cells of the automaton, and in each time unit each cell receives information about the current state of the cells to which it is connected. The cellular automaton evolve according a transition rule that specifies the current possible states of each cell as a function of the preceding state of the cell and the states of the connected cells." (Francesc S Beltran et al, "A Language Shift Simulation Based on Cellular Automata", 2011)

"Cellular automata (CA) are idealizations of physical systems in which both space and time are assumed to be discrete and each of the interacting units can have only a finite number of discrete states." (Andreas Schadschneider et al, "Vehicular Traffic II: The Nagel–Schreckenberg Model" , 2011)

"Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields." (Francesco Berto & Jacopo Tagliabue, "Cellular Automata", Stanford Encyclopedia of Philosophy, 2012) 

🕸Systems Engineering: Bifurcation (Definitions)

"A bifurcation is an event that occurs in the evolution of a dynamic system in which the characteristic behavior of the system is transformed. This occurs when an attractor in the system changes in response to change in the value of a parameter." (Courtney Brown, "Chaos and Catastrophe Theories", 1995)

"A qualitative change in a system’s dynamics as a parameter is varied. One-parameter bifurcation diagrams often depict invariant sets of the dynamics against a single parameter, indicating stability and any bifurcation points. Two-parameter bifurcation diagrams depict curves in a parameter plane on which one-parameter bifurcations occur." (Alan Champneys, "Dynamics of Parametric Excitation", 2009) 

"A qualitative change in the essential behavior of a mathematical system (e. g., algebraic equations, iterated maps, differential equations), as a parameter is varied. Usually involves an abrupt appearance and/or disappearance of solutions." (Oded Regev, "Chaos and Complexity in Astrophysics", 2009) 

"Bifurcation is a qualitative change of the phase portrait." (George Osipenko, "Center Manifolds", 2009) 

"In parametrized dynamical systems a bifurcation occurs when a qualitative change is invoked by a change of parameters. In models such a qualitative change corresponds to transition between dynamical regimes. In the generic theory a finite list of cases is obtained, containing elements like ‘saddle-node’, ‘period doubling’, ‘Hopf bifurcation’ and many others." (Henk W Broer & Heinz Hanssmann, "Hamiltonian Perturbation Theory (and Transition to Chaos)", 2009) 

"In mathematical models, a bifurcation occurs when a small change made to a parameter value of a system causes a sudden qualitative or topological change in its behavior." (Dmitriy Laschov & Michael Margaliot, "Mathematical Modeling of the λ Switch: A Fuzzy Logic Approach", 2010)

"In dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behaviour. Generally, at a bifurcation, the local stability properties of equilibria, periodic orbits or other invariant sets changes." (Gregory Faye, "An introduction to bifurcation theory",  2011)

"Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. Bifurcations can occur in both continuous systems (described by ODEs, DDEs, or PDEs) and discrete systems (described by maps)." (Tianshou Zhou, "Bifurcation", 2013)

"Roughly speaking, refers to the phenomenon of a system exhibiting new dynamical behavior as the parameter is varied." (Wei-Bin Zhang, "Chaos in Economics", 2014)

"A sudden change that accompanies the onset of chaos at a critical value of a varied control parameter." (Viet-Thanh Pham et al, "Chaotic Attractor in a Novel Time-Delayed System with a Saturation Function", 2015) 

"A qualitative change in the behavior of a dynamic system." (Ben Tran, "Enneagram through Chaos Theory", 2016)

🔬Data Science: Fractal (Definitions)

"A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales [...]" (Benoît Mandelbrot, "The Fractal Geometry of Nature", 1982)

"Objects (in particular, figures) that have the same appearance when they are seen on fine and coarse scales." (David Rincón & Sebastià Sallent, Scaling Properties of Network Traffic, 2008) 

"A collection of objects that have a power-law dependence of number on size." (Donald L Turcotte, "Fractals in Geology and Geophysics", 2009) 

"A fractal is a geometric object which is self-similar and characterized by an effective dimension which is not an integer." (Leonard M Sander, "Fractal Growth Processes", 2009) 

"A fractal is a structure which can be subdivided into parts, where the shape of each part is similar to that of the original structure." (Yakov M Strelniker, "Fractals and Percolation", 2009) 

"A fractal is an image that comprises two distinct attributes: infinite detail and self-similarity." (Daniel C Doolan et al, "Unlocking the Hidden Power of the Mobile", 2009)

"A geometrical object that is invariant at any scale of magnification or reduction." (Sidney Redner, "Fractal and Multifractal Scaling of Electrical Conduction in Random Resistor Networks", 2009) 

[Fractal structure:] "A pattern or arrangement of system elements that are self-similar at different spatial scales." (Michael Batty, "Cities as Complex Systems: Scaling, Interaction, Networks, Dynamics and Urban Morphologies", 2009) 

"A set whose (suitably defined) geometrical dimensionis non-integral. Typically, the set appears selfsimilar on all scales. A number of geometrical objects associated with chaos (e. g. strange attractors) are fractals." (Oded Regev, "Chaos and Complexity in Astrophysics", 2009) 

[Fractal system:] "A system characterized by a scaling law with a fractal, i. e., non-integer exponent. Fractal systems are self-similar, i. e., a magnification of a small part is statistically equivalent to the whole." (Jan W Kantelhardt, "Fractal and Multifractal Time Series", 2009) 

"An adjective or a noun representing complex configurations having scale-free characteristics or self-similar properties. Mathematically, any fractal can be characterized by a power law distribution." (Misako Takayasu & Hideki Takayasu, "Fractals and Economics", 2009) 

"Fractals are complex mathematical objects that are invariant with respect to dilations (self-similarity) and therefore do not possess a characteristic length scale. Fractal objects display scale-invariance properties that can either fluctuate from point to point (multifractal) or be homogeneous (monofractal). Mathematically, these properties should hold over all scales. However, in the real world, there are necessarily lower and upper bounds over which self-similarity applies." (Alain Arneodo et al, "Fractals and Wavelets: What Can We Learn on Transcription and Replication from Wavelet-Based Multifractal Analysis of DNA Sequences?", 2009) 

"Mathematical object usually having a geometrical representation and whose spatial dimension is not an integer. The relation between the size of the object and its “mass” does not obey that of usual geometrical objects." (Bastien Chopard, "Cellular Automata: Modeling of Physical Systems", 2009) 

 "A fragmented geometric shape that can be split up into secondary pieces, each of which is approximately a smaller replica of the whole, the phenomenon commonly known as self similarity." (Khondekar et al, "Soft Computing Based Statistical Time Series Analysis, Characterization of Chaos Theory, and Theory of Fractals", 2013) 

 "A natural phenomenon or a mathematical set that exhibits a repeating pattern which can be replicated at every scale." (Rohnn B Sanderson, "Understanding Chaos as an Indicator of Economic Stability", 2016) 

 "Geometric pattern repeated at progressively smaller scales, where each iteration is about a reproduction of the image to produce completely irregular shapes and surfaces that can not be represented by classical geometry. Fractals are generally self-similar (each section looks at all) and are not subordinated to a specific scale. They are used especially in the digital modeling of irregular patterns and structures in nature." (Mauro Chiarella, Folds and Refolds: Space Generation, Shapes, and Complex Components, 2016)

🕸Systems Engineering: Chaos (Definitions)

"Long-term unpredictable behaviour caused by sensitive dependence on initial conditions." (Jesús B A Hernández & Patricia H Rodríguez, "Nonlinear Techniques for Signals Characterization", 2009)

"The effect whereby minor deficiencies or miniscule changes occurring in any phase of the project, but particularly in the beginning of a process, create significantly different outcomes." (José L Fernández-Solís & Iván Mutis, "The Idealization of an Integrated BIM, Lean, and Green Model (BLG)", 2010)

"A situation where a complex and random-looking behavior arises from simple nonlinear deterministic systems with sensitive dependence on initial conditions." (Bellie Sivakumar, "Chaos Theory for Hydrologic Modeling and Forecasting: Progress and Challenges", 2011)

"An interesting deterministic experience which has a random and unpredictable apparent behavior where petite changes in the initial conditions can lead to immense changes over time." (Mofazzal H. Khondekar et al, "Soft Computing Based Statistical Time Series Analysis, Characterization of Chaos Theory, and Theory of Fractals", 2013)

"A nonlinear erratic phenomenon that is found to be exhibited in several physical systems." (Hassène Gritli, "Further Investigation of the Period-Three Route to Chaos in the Passive Compass-Gait Biped Model", 2015)

"A type of behavior of a deterministic nonlinear system, where tiny changes in initial conditions make huge changes over time." (Viet-Thanh Pham et al, "Chaotic Attractor in a Novel Time-Delayed System with a Saturation Function", 2015)

"The type of behavior of a complex system, where tiny changes in a system’s initial conditions can lead to very large changes over time." (Christos Volos, "Random Bit Generator Based on Non-Autonomous Chaotic Systems", 2015)

"A state of disorder where each unit of a system behaves independently from each other at the same point of time." (Simanti Bhattacharya & Angshuman Bagchi, "Cellular Automata-Basics: Applications in Problem Solving", 2016)

"A new branch of science that deals with systems whose evolution depends very sensitively upon the initial conditions." (Wassim J Aloulou, "Understanding Entrepreneurship through Chaos and Complexity Perspectives", 2016)

🕸Systems Engineering: Systems Engineering (Just the Quotes)

"The engineer must be able not only to design, but to execute. A draftsman may be able to design, but unless he is able to execute his designs to successful operation he cannot be classed as an engineer. The production engineer must be able to execute his work as he has planned it. This requires two qualifications in addition to technical engineering ability: He must know men, and he must have creative ability in applying good statistical, accounting, and 'system' methods to any particular production work he may undertake." (Hugo Diemer, "Industrial Engineering", 1905)

"The analysis of engineering systems and the understanding of economic structure have advanced since then, and the time is now more ripe to bring these topics into a potentially fruitful marriage." (Arnold Tustin, "The Mechanism of Economic Systems", 1953)

"The term 'systems engineering' is a term with an air of romance and of mystery. The romance and the mystery come from its use in the field of guided missiles, rockets, artificial satellites, and space flight. Much of the work being done in these areas is classified and hence much of it is not known to the general public or to this writer. […] From a business point of view, systems engineering is the creation of a deliberate combination of human services, material services, and machine service to accomplish an information processing job. But this is also very nearly a definition of business system analysis. The difference, from a business point of view, therefore, between business system analysis and systems engineering is only one of degree. In general, systems engineering is more total and more goal-oriented in its approach [...]." ("Computers and People" Vol. 5, 1956)

"By some definitions 'systems engineering' is suggested to be a new discovery. Actually it is a common engineering approach which has taken on a new and important meaning because of the greater complexity and scope of problems to be solved in industry, business, and the military. Newly discovered scientific phenomena, new machines and equipment, greater speed of communications, increased production capacity, the demand for control over ever-extending areas under constantly changing conditions, and the resultant complex interactions, all have created a tremendously accelerating need for improved systems engineering. Systems engineering can be complex, but is simply defined as 'logical engineering within physical, economic and technical limits' - bridging the gap from fundamental laws to a practical operating system." (Instrumentation Technology, 1957)

"Systems engineering embraces every scientific and technical concept known, including economics, management, operations, maintenance, etc. It is the job of integrating an entire problem or problem to arrive at one overall answer, and the breaking down of this answer into defined units which are selected to function compatibly to achieve the specified objectives. [...] Instrument and control engineering is but one aspect of systems engineering - a vitally important and highly publicized aspect, because the ability to create automatic controls within overall systems has made it possible to achieve objectives never before attainable, While automatic controls are vital to systems which are to be controlled, every aspect of a system is essential. Systems engineering is unbiased, it demands only what is logically required. Control engineers have been the leaders in pulling together a systems approach in the various technologies." (Instrumentation Technology, 1957) 

"Systems engineering is more likely to be closely associated with top management of an enterprise than the engineering of the components of the system. If an engineering task is large and complex enough, the arrangement-making problem is especially difficult. Commonly, in a large job, the first and foremost problem for the systems engineers is to relate the objectives to the technical art. [...] Systems engineering is a highly technical pursuit and if a nontechnical man attempts to direct the systems engineering as such, it must end up in a waste of technical talent below." (Aeronautical Engineering Review Vol. 16, 1957) 

"Systems engineering is the name given to engineering activity which considers the overall behavior of a system, or more generally which considers all factors bearing on a problem, and the systems approach to control engineering problems is correspondingly that approach which examines the total dynamic behavior of an integrated system. It is concerned more with quality of performance than with sizes, capacities, or efficiencies, although in the most general sense systems engineering is concerned with overall, comprehensive appraisal." (Ernest F Johnson, "Automatic process control", 1958)

"There are two types of systems engineering - basis and applied. [...] Systems engineering is, obviously, the engineering of a system. It usually, but not always, includes dynamic analysis, mathematical models, simulation, linear programming, data logging, computing, optimating, etc., etc. It connotes an optimum method, realized by modern engineering techniques. Basic systems engineering includes not only the control system but also all equipments within the system, including all host equipments for the control system. Applications engineering is - and always has been - all the engineering required to apply the hardware of a hardware manufacturer to the needs of the customer. Such applications engineering may include, and always has included where needed, dynamic analysis, mathematical models, simulation, linear programming, data logging, computing, and any technique needed to meet the end purpose - the fitting of an existing line of production hardware to a customer's needs. This is applied systems engineering." (Instruments and Control Systems Vol. 31, 1958)

"In a society which is producing more people, more materials, more things, and more information than ever before, systems engineering is indispensable in meeting the challenge of complexity." (Harold Chestnut, "Systems Engineering Tools," 1965)

"Systems engineering is most effectively conceived of as a process that starts with the detection of a problem and continues through problem definition, planning and designing of a system, manufacturing or other implementing section, its use, and finally on to its obsolescence. Further, Systems engineering is not a matter of tools alone; It is a careful coordination of process, tools and people." (Arthur D. Hall, "Systems Engineering from an Engineering Viewpoint" In: Systems Science and Cybernetics. Vol.1 Issue.1, 1965)

"Systems Engineering Methods is directed towards the development of a broad systems engineering approach to help such people improve their decision-making capability. Although the emphasis is on engineering, the systems approach can also has validity for many other areas in which emphasis may be social, economic, or political." (Harold Chestnut, "Systems Engineering Methods", 1965) 

"The Systems engineering method recognizes each system is an integrated whole even though composed of diverse, specialized structures and sub-functions. It further recognizes that any system has a number of objectives and that the balance between them may differ widely from system to system. The methods seek to optimize the overall system functions according to the weighted objectives and to achieve maximum compatibility of its parts." (Harold Chestnut, "Systems Engineering Tools," 1965)

"In the minds of many writers systems engineering is synonymous with component selection and interface design; that is, the systems engineer does not design hardware but decides what types of existing hardware shall be coupled and how they shall be coupled. Complete agreement that this function is the essence of systems engineering will not be found here, for, besides the very important function of systems engineering in systems analysis, there is the role played by systems engineering in providing boundary conditions for hardware design." (A Wayne Wymore, "A Mathematical Theory of Systems Engineering", 1967)

"Only if mathematical rigor is adhered to, can systems problems be dealt with effectively, and so it is that the systems engineer must, at least, develop an appreciation for mathematical rigor if not also considerable mathematical competence." (A Wayne Wymore, "A Mathematical Theory of Systems Engineering", 1967)

"Systems Engineering is the science of designing complex systems in their totality to ensure that the component sub-systems making up the system are designed, fitted together, checked and operated in the most efficient way." (Gwilym Jenkins, "The Systems Approach", 1969) 

"The purpose and real value of systems engineering is [...] to keep going around the loop; find inadequacies and make improvements." (Robert E Machol, "Mathematicians are useful", 1971)

"System engineering is a robust approach to the design, creation, and operation of systems. In simple terms, the approach consists of identification and quantification of system goals, creation of alternative system design concepts, performance of design trades, selection and implementation of the best design, verification that the design is properly built and integrated, and post-implementation assessment of how well the system meets (or met) the goals." (NASA, "NASA Systems Engineering Handbook", 1995) 

"System engineering is the art and science of creating effective systems, using whole system, whole life principles." (Derek Hitchins, 1995)

"With the subsequent strong support from cybernetics, the concepts of systems thinking and systems theory became integral parts of the established scientific language, and led to numerous new methodologies and applications - systems engineering, systems analysis, systems dynamics, and so on." (Fritjof Capra, "The Web of Life", 1996)

"Systems engineering differs from traditional disciplines in that (1) it is focused on the system as a whole; (2) it is concerned with customer needs and operational environment; (3) it leads system conceptual design; and (4) it bridges traditional engineering disciplines and gaps between specialties. Moreover, systems engineering is an integral part of project management in that it plans and guides the engineering effort." (Alexander Kossiakoff et al, "Systems Engineering: Principles and practice" 2nd Ed., 2003)

"Systems engineering is an inherent part of project management - the part that is concerned with guiding the engineering effort itself - setting its objectives, guiding its execution, evaluating its results, and prescribing necessary corrective actions to keep it on course." (Alexander Kossiakoff et al, "Systems Engineering: Principles and practice" 2nd Ed., 2003)

"Systems engineering is focused on the system as a whole; it emphasizes its total operation. It looks at the system from the outside, that is, at its interactions with other systems and the environment, as well as from the inside. It is concerned not only with the engineering design of the system but also with external factors, which can significantly constrain the design." (Alexander Kossiakoff et al, "Systems Engineering: Principles and practice" 2nd Ed., 2003)

"It is no longer sufficient for engineers merely to design boxes such as computers with the expectation that they would become components of larger, more complex systems. That is wasteful because frequently the box component is a bad fit in the system and has to be redesigned or worse, can lead to system failure. We must learn how to design large-scale, complex systems from the top down so that the specification for each component is derivable from the requirements for the overall system. We must also take a much larger view of systems. We must design the man-machine interfaces and even the system-society interfaces. Systems engineers must be trained for the design of large-scale, complex, man-machine-social systems." (A Wayne Wymore, "Systems Movement: Autobiographical Retrospectives", 2004)

"The basic idea of systems engineering is that it is possible to take a large and highly complex system that one wants to build, separate it into key parts, give the parts to different groups of people to work on, and coordinate their development so that they can be put together at the end of the process. This mechanism is designed to be applied recursively, so that we separate the large system into parts, then the parts into smaller parts, until each part is small enough for one person to execute. Then we put all of the parts together until the entire system works." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)

"Systems engineering should be, first and foremost, a state of mind and an attitude taken when dealing with complexity." (Dominique Luzeaux et al, "Complex Systems and Systems of Systems Engineering", 2013) 

"The central activity of engineering, as distinguished from science, is the design of new devices, processes and systems." (Myron Tribus, "Rational Descriptions, Decisions and Designs", 2016)

"Over-engineering is a real disease of many engineers as they delight in design purity and ignore tradeoffs." (Alex Xu, "System Design Interview: An insider's guide", 2017)

"If all the theories pertinent to systems engineering could be discussed within a common framework by means of a standard set of nomenclature and definitions, many separate courses might not be required." (A Wayne Wymore)

🕸Systems Engineering: Causal Map (Definitions)

"Causal maps are representations of individuals (or groups) beliefs about causal relations. They include elements, with only two kinds of properties. The first property is 'relevance'. The second  is the possibility of being in one (of two) 'influence relationships' (positive or negative) with one (of three) strengths (weak. moderate, or strong)." (Kivia Markoczy & Jeff Goldberg, "A method for eliciting and comparing causal maps", 1995)

"A causal map is an abstract representation of the causal relationships among kinds of objects and events in the world. Such relationships are not, for the most part, directly observable, but they can often be accurately inferred from observations." (Alison Gopnik & Clark Glymour, "Causal maps and Bayes nets: a cognitive and computational account of theory-formation" [in "The cognitive basis of science"], 2002)

"A causal map (also called an influence diagram or a cause map) is a directed graph in which causal concepts (or nodes) represent the important variables that make up a domain." (S Nadkarni, Aggregated causal maps: An approach to elicit and aggregate the knowledge of multiple experts, 2003) 

"A causal map is a directed graph that represents an individual’s (an agent, a group of agents or an organization) assertions about its beliefs with respect to its environment." (Nassreddine Garoui & Anis Jarboui, "Cognitive Mapping: Testing Application of Causal Algebra", Applied Mathematics Vol.3 (4),  2012)

"A causal map is a two-dimensional network of nodes and links that conveys the  hierarchical and cause-effect relationships between events or variables within a complex system." (Allan Jeong & Woon Jee Lee, "The Sequential Analysis, Modeling and Visualization of Collaborative Causal Mapping Processes and Effects on Causal Understanding", 2013)

"A word-and-arrow (or statement-and-arrow) diagram in which ideas are causally linked to one another through the use of arrows. The arrows indicate how one idea or action leads to another in a means-ends relationship; in other words, an arrow means 'might cause', 'might lead to', 'might result in', or some other kind of influence relationship." (Fran Ackermann et al, "Visual Strategy: Strategy Mapping for Public and Nonprofit Organizations", 2014)

"A visual depiction of where certain kinds of data exist across an organization. Example: we have produced a data map showing where all customer data exists across our systems." (Gregory Lampshire, "The Data and Analytics Playbook", 2016)

"A Causal Map is hierarchical in structure (linking means to ends) and built with a focus on achieving goals. The process of creating the maps is ideally a group process and this in itself will add lots of value to a collective understanding of goals around EDI, what is required to achieve these and some of the potential challenges around this." (Nicola Morrill, "Supporting Your Efforts on Diversity", 2021)

🕸Systems Engineering: Resilience (Definitions)

"The ability of a system, community, or society exposed to hazards to resist, absorb, accommodate to and recover from the effects of a hazard in a timely and efficient manner, including through the preservation and restoration of its essential basic structures and functions." (ISDR, 2009)

"The quality of being able to absorb systemic 'shocks' without being destroyed even if recovery produces an altered state to that of the status quo ante." (Philip Cooke, "Regional Innovation Systems in Centralised States: Challenges, Chances, and Crossovers", 2015)

"A swarm is resilient if the loss of individual agents has little impact on the success of the task of the swarm." (Thalia M Laing et al, "Security in Swarm Robotics", 2016)

"Resilience is the capacity of organism or system to withstand stress and catastrophe." (Sunil L Londhe, "Climate Change and Agriculture: Impacts, Adoption, and Mitigation", 2016)

"System resilience is an ability of the system to withstand a major disruption within acceptable degradation parameters and to recover within an acceptable time." (Denis Čaleta, "Cyber Threats to Critical Infrastructure Protection: Public Private Aspects of Resilience", 2016) 

"The capacity for self-organization, and to adapt to impact factors." (Ahmed Karmaoui, Environmental Vulnerability to Climate Change in Mediterranean Basin: Socio-Ecological Interactions between North and South, 2016)

"The capacity of ecosystem to absorb disturbance, reorganize and return to an equilibrium or steady-state while undergoing some change or perturbation so that still retain essentially the same function, structure, identity, and feedbacks." (Susmita Lahiri et al, "Role of Microbes in Eco-Remediation of Perturbed Aquatic Ecosystem", 2017)

"A capability to anticipate, prepare for, respond to, and recover from significant multi-hazard threats with minimum damage to social well-being, the economy, and the environment." (Carolyn N Stevenson, "Addressing the Sustainable Development Goals Through Environmental Education", 2019)

"The conventional understanding of resilience applied to socioeconomic studies regards the bouncing-back ability of a socioeconomic system to recover from a shock or disruption. Today resilience is being influenced by an evolutionary perspective, underlining it as the bouncing-forward ability of the system to undergo anticipatory or reactionary reorganization to minimize the impact of destabilizing shocks and create new growth trajectories." (Hugo Pinto & André Guerreiro, "Resilience, Innovation, and Knowledge Transfer: Conceptual Considerations and Future Research Directions", 2019)

"Is the system capacity to rebalance after a perturbation." (Ahmed Karmaoui et al, "Composite Indicators as Decision Support Method for Flood Analysis: Flood Vulnerability Index Category", 2020)

"The ability of human or natural systems to cope with adverse events and be able to effect a quick recovery." (Maria F Casado-Claro, "Fostering Resilience by Empowering Entrepreneurs and Small Businesses in Local Communities in Post-Disaster Scenarios", 2021)

"The word resilience refers to the ability to overcome critical moments and adapt after experiencing some unusual and unexpected situation. It also indicates return to normal." (José G Vargas-Hernández, "Urban Socio-Ecosystems Green Resilience", 2021)