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A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]
Complex systems is a scientific field that studies the common properties of systems considered complex in nature, society, and science. It is also called complex systems theory, complexity science, study of complex systems and/or sciences of complexity. The key problems of such systems are difficulties with their formal modeling and simulation ...
This is a list of dynamical system and differential equation topics, by Wikipedia page. See also list of partial differential equation topics , list of equations . Dynamical systems, in general
Linear dynamical systems can be solved exactly, in contrast to most nonlinear ones. Occasionally, a nonlinear system can be solved exactly by a change of variables to a linear system. Moreover, the solutions of (almost) any nonlinear system can be well-approximated by an equivalent linear system near its fixed points. Hence, understanding ...
Steady state: A state in which the variables (called state variables) which define the behavior of a system or a process are unchanging in time. In chemistry, it is a more general situation than dynamic equilibrium. If a system is in steady state then the recently observed behaviour of the system will continue into the future. In stochastic ...
In mathematics, symbolic dynamics is the study of dynamical systems defined on a discrete space consisting of infinite sequences of abstract symbols. The evolution of the dynamical system is defined as a simple shift of the sequence. Because of their explicit, discrete nature, such systems are often relatively easy to characterize and understand.
Complex systems biology is a field of science that studies the emergence of complexity in functional organisms from the viewpoint of dynamic systems theory. [20] The latter is also often called systems biology and aims to understand the most fundamental aspects of life.
An example of a random dynamical system is a stochastic differential equation; in this case the distribution Q is typically determined by noise terms. It consists of a base flow, the "noise", and a cocycle dynamical system on the "physical" phase space. Another example is discrete state random dynamical system; some elementary ...