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List Of Dynamical System Topics
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 *Deterministic system (mathematics) *Linear system *Partial differential equation *Dynamical systems and chaos theory *Chaos theory ** Chaos argument ** Butterfly effect ** 0-1 test for chaos *Bifurcation diagram * Feigenbaum constant *Sharkovskii's theorem *Attractor **Strange nonchaotic attractor *Stability theory **Mechanical equilibrium **Astable ** Monostable **Bistability **Metastability *Feedback **Negative feedback **Positive feedback **Homeostasis *Damping ratio *Dissipative system *Spontaneous symmetry breaking *Turbulence *Perturbation theory *Control theory ** Non-linear control **Adaptive control ** Hierarchical control **Intelligent control ** Optimal control **Dynamic programming **Robust control ** Stochastic control *System dynamics, system analysis * Takens' theorem * Exponen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Dynamical System
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it. At any given time, a dynamical system has a state representing a point in an appropriate state space. This state is often given by a tuple of real numbers or by a vector in a geome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Stability Theory
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance. In dynamical systems, an orbit is called '' Lyapunov stable'' if the forward orbit of any point is in a small enough neighborhood or it stays in a small (but perhaps, larger) neighborhood. Various criteria have been developed to prove stability or instability of an orbit. Under favorable circumstances, the question may be reduced to a well-studied problem invo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |