Ads
related to: discrete dynamical systems pdf file viewerpdf-format.com has been visited by 100K+ users in the past month
Search results
Results from the WOW.Com Content Network
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
There are many forms of these maps, [2] many of which are equivalent under a coordinate transformation. For example two of the most common ones are: : +: The second one can be mapped to the first using the fact that . = + (), so : + is the same under the transformation = + ().
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]
In control engineering, a discrete-event dynamic system (DEDS) is a discrete-state, event-driven system of which the state evolution depends entirely on the occurrence of asynchronous discrete events over time.
For discrete dynamical systems, consider the system + = (,). Then a local bifurcation occurs at (,) if the matrix , has an eigenvalue with modulus equal to one. If the eigenvalue is equal to one, the bifurcation is either a saddle-node (often called fold bifurcation in maps), transcritical or pitchfork bifurcation.
In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions, as the system evolves.
Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions . Chaotic maps often occur in the study of dynamical systems .
In the mathematical field of dynamical systems, a random dynamical system is a dynamical system in which the equations of motion have an element of randomness to them. Random dynamical systems are characterized by a state space S, a set of maps from S into itself that can be thought of as the set of all possible equations of motion, and a probability distribution Q on the set that represents ...
Ads
related to: discrete dynamical systems pdf file viewerpdf-format.com has been visited by 100K+ users in the past month