Roughly speaking, an attracting set for a dynamical system is a closed subset A of its phase space such that for "many" choices of initial point the system will evolve towards A .
Swarm intelligence is the discipline that deals with natural and artificial systems composed of many individuals that coordinate using decentralized control and self-organization.
A bifurcation of a dynamical system is a qualitative change in its dynamics produced by varying parameters.
In numerical analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference schemes as applied to linear partial differential equations.
A time series is a sequence of data points, typically consisting of successive measurements made over a time interval. Examples of time series are ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. Time series are very frequently plotted via line charts.
In mathematics, an ordinary differential equation or ODE is an equation containing a function or functions of oneindependent variable and its derivatives. The term "ordinary" is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
In mathematics, the Gauss map (also known as Gaussian map or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:
In mathematics and physics, a phase space of a dynamical system is a space in which all possible states of asystem are represented, with each possible state of the system corresponding to one unique point in the phase space.
Population dynamics is the branch of life sciences that studies short-term and long-term changes in the size and age composition of populations, and the biological and environmental processes influencing those changes.
A coupled map lattice (CML) is a dynamical system that models the behavior of non-linear systems (especially partial differential equations). They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems. This includes the dynamics of spatiotemporal chaos where the number of effective degrees of freedom diverges as the size of the system increases.
Chaos theory is the field of study in mathematics that studies the behavior of dynamical systems that are highly sensitive to initial conditions—a response popularly referred to as the butterfly effect.
Homeostasis, also spelled homoeostasis (from Greek: ὅμοιος homœos, "similar" and στάσις stasis, "standing still"), is the property of a system in which variables are regulated so that internal conditions remain stable and relatively constant. Examples of homeostasis include the regulation of temperature and the balance between acidity and alkalinity (pH). It is a process that maintains the stability of the human body's internal environment in response to changes in external conditions.
Self-reference occurs in natural or formal languages when a sentence, idea or formula refers to itself. The reference may be expressed either directly—through some intermediate sentence or formula—or by means of some encoding.
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop.
Cybernetics is a transdisciplinary approach for exploring regulatory systems, their structures, constraints, and possibilities.
Cybernetics is relevant to the study of systems, such as mechanical, physical, biological, cognitive, and social systems.
Information theory is a branch of applied mathematics, electrical engineering, and computer science involving the quantification of information.
In theoretical computer science and mathematics, the theory of computation is the branch that deals with how efficiently problems can be solved on a model of computation, using an algorithm.
"Autopoiesis" (from Greek αὐτo- (auto-), meaning "self", and ποίησις (poiesis), meaning "creation, production") refers to asystem capable of reproducing and maintaining itself. The term was introduced in 1972 by Chilean biologists Humberto Maturana and Francisco Varela to define the self-maintaining chemistry of living cells. Since then the concept has been also applied to the fields of systems theory and sociology.
Sensemaking is the process by which people give meaning to experience. While this process has been studied by other disciplines under other names for centuries, the term "sensemaking" has primarily marked three distinct but related research areas since the 1970s: Sensemaking was introduced to Human–computer interaction by PARC researchers Russell, Stefik, Pirolli and Card in 1993, to information science by Brenda Dervin, and to organizational studies by Karl Weick.
In thermodynamics, entropy (usual symbol S) is a measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder. According to the second law of thermodynamics the entropy of an isolated system never decreases; such a system will spontaneously proceed towards thermodynamic equilibrium, the configuration with maximum entropy. Systems that are not isolated may decrease in entropy, provided they increase the entropy of their environment by at least that same amount. Since entropy is a state function, the change in the entropy of a system is the same for any process that goes from a given initial state to a given final state, whether the process is reversible or irreversible. However, irreversible processes increase the combined entropy of the system and its environment.
System dynamics is an approach to understanding the nonlinear behaviour of complex systems over time using stocks and flows, internal feedback loops and time delays
Machine learning is a subfield of computer sciencethat evolved from the study of pattern r
Artificial life (often abbreviated ALife or A-Life) is a field of study and an associated art form which examine systems related to life, its processes, and its evolution, through the use of simulations with computer models, robotics, and biochemistry.
In machine learning and cognitive science, artificial neural networks (ANNs) are a family of statistical learning models inspired by biological neural networks (the central nervous systems of animals, in particular the brain) and are used to estimate or approximate functions that can depend on a large number of inputs and are generally unknown. Artificial neural networks are generally presented as systems of interconnected "neurons" which send messages to each other. The connections have numeric weights that can be tuned based on experience, making neural nets adaptive to inputs and capable of learning.
In computer science, evolutionary computation (a.k.a. evolutionary computing) is a subfield of artificial intelligence (more particularly computational intelligence) that can be defined by the type of algorithms it is concerned with. These algorithms, called evolutionary algorithms, are based on adopting Darwinian principles, hence the name. Technically they belong to the family of trial and error problem solvers and can be considered global optimization methods with ametaheuristic or stochastic optimization character, distinguished by the use of a population of candidate solutions (rather than just iterating over one point in the search space). They are mostly applied for black box problems (no derivatives known), often in the context of expensive optimization.
In the field of artificial intelligence, a genetic algorithm (GA) is a search heuristic that mimics the process of natural selection. This heuristic (also sometimes called a metaheuristic) is routinely used to generate useful solutions to optimizationand search problems. Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover.
Evolutionary developmental biology (evolution of development or informally, evo-devo) is a field of biology that compares the developmental processes of different organisms to determine the ancestral relationship between them, and to discover how developmental processes evolved. It addresses the origin and evolution of embryonic development; how modifications of development and developmental processes lead to the production of novel features, such as the evolution of feathers; the role of developmental plasticity in evolution; how ecology impacts development and evolutionary change; and the developmental basis of homoplasy and homology.
Artificial intelligence (AI) is the intelligence exhibited by machines or software. It is also the name of the academic field of study which studies how to create computers and computer software that are capable of intelligent behavior.
Evolutionary robotics (ER) is a methodology that uses evolutionary computation to develop controllers for autonomous robots.
A fractal is a natural phenomenon or a mathematical set that exhibits a repeating pattern that displays at every scale.
Reaction–diffusion systems are mathematical models which explain how the concentration of one or more substances distributed in space changes under the influence of two processes: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space.
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
A dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter.
A dissipative structure is a dissipative system that has a dynamical régime that is in some sense in a reproducible steady state. This reproducible steady state may be reached by natural evolution of the system, by artifice, or by a combination of these two.
In physics, chemistry and materials science, percolation (from Lat. percōlāre, to filter or trickle through) refers to the movement and filtering of fluids through porous materials.
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model studied in computability theory,mathematics, physics, complexity science, theoretical biology and microstructure modeling. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tessellation structures, and iterative arrays
Self-replication is any behavior of a dynamical system that yields construction of an identical copy of itself. Biological cells, given suitable environments, reproduce by cell division.
Geomorphology (from Greek: γῆ, ge, "earth"; μορφή, morfé, "form"; and λόγος, logos, "study") is the scientific study of the origin and evolution of topographic and bathymetric features created by physical or chemical processes operating at or near the earth's surface.
Spatial ecology is a specialization in ecology and geography that is concerned with the identification of spatial patterns and their relationships to ecological phenomena.
scale-free network is a network whose degree distribution follows a power law, at least asymptotically.
A small-world network is a type of mathematical graph in which most nodes are not neighbors of one another, but most nodes can be reached from every other by a small number of hops or steps.
Social network analysis (SNA) is a strategy for investigating social structures through the use of network and graphtheories. It characterizes networked structures in terms of nodes (individual actors, people, or things within the network) and the ties or edges (relationships or interactions) that connect them.
In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed insocial network analysis, and many of the terms used to measure centrality reflect their sociological origin.
In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A "graph" in this context is made up of "vertices" or "nodes" and lines callededges that connect them.
Scalability is the ability of a system, network, or process to handle a growing amount of work in a capable manner or its ability to be enlarged to accommodate that growth
All networks, including biological networks, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as graphs, which include a wide variety of subgraphs. One important local property of networks are so-called network motifs, which are defined as recurrent and statistically significantsub-graphs or patterns.
Systems biology is the computational and mathematical modeling of complex biological systems.
Dynamic network analysis (DNA) is an emergent scientific field that brings together traditional social network analysis (SNA), link analysis (LA), social simulationand multi-agent systems (MAS) within network science and network theory.
Social dynamics can refer to the behavior of groups that results from the interactions of individual group members as well to the study of the relationship between individual interactions and group level behaviors.
Collective intelligence is shared or group intelligence that emerges from the collaboration, collective efforts, and competition of many individuals and appears inconsensus decision making.
Self-organized criticality is an abrupt disturbance in a system resulting from a buildup of events without external stimuli
Herd mentality, or mob mentality, describes how people are influenced by their peers to adopt certain behaviors, follow trends, and/or purchase items. Examples of the herd mentality include stock market trends, superstition, home décor, etc. Social psychologists study the related topics of group intelligence, crowd wisdom, and decentralized decision making.
An agent-based model (ABM) is one of a class of computational models for simulating the actions and interactions of autonomous agents (both individual or collective entities such as organizations or groups) with a view to assessing their effects on the system as a whole. It combines elements of game theory, complex systems, emergence, computational sociology, multi-agent systems, and evolutionary programming.
In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs.
Swarm behaviour, or swarming, is a collective behaviour exhibited by animals of similar size which aggregate together, perhaps milling about the same spot or perhaps moving en masse or migrating in some direction.
ynchronization is the coordination of events to operate a system in unison. The familiar conductor of an orchestra serves to keep the orchestra in time. Systems operating with all their parts in synchrony are said to be synchronous or in sync.
In computer science, particle swarm optimization (PSO) is a computational method that optimizes a problem by iteratively trying to improve a candidate solutionwith regard to a given measure of quality.
The prisoner's dilemma is a canonical example of a game analyzed in game theory that shows why two purely "rational" individuals might not cooperate, even if it appears that it is in their best interests to do so.
Evolutionary game theory (EGT) is the application of game theory to evolving populations of lifeforms in biology. EGT is useful in this context by defining a framework of contests, strategies, and analytics into which Darwinian competition can be modelled.
Competition in biology and sociology, is a contest between organisms, animals, individuals, groups, etc., forterritory, a niche, or a location of resources, for resources and goods, mates, for prestige, recognition, awards, or group or social status, for leadership. Competition is the opposite of cooperation.
Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the information they have, the cognitive limitations of their minds, and the time available to make the decision.
Irrationality is cognition, thinking, talking or acting without inclusion of rationality. It is more specifically described as an action or opinion given through inadequate use of reason, emotional distress, or cognitive deficiency.