Search results
Results from the WOW.Com Content Network
In dynamical systems theory, the Bogdanov map is a chaotic 2D map related to the Bogdanov–Takens bifurcation. It is given by the transformation: It is given by the transformation: { x n + 1 = x n + y n + 1 y n + 1 = y n + ϵ y n + k x n ( x n − 1 ) + μ x n y n {\displaystyle {\begin{cases}x_{n+1}=x_{n}+y_{n+1}\\y_{n+1}=y_{n}+\epsilon y_{n ...
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior.Maps may be parameterized by a discrete-time or a continuous-time parameter.
This progression is known as the intermittency route to chaos. Pomeau and Manneville described three routes to intermittency where a nearly periodic system shows irregularly spaced bursts of chaos. [ 3 ] These (type I, II and III) correspond to the approach to a saddle-node bifurcation , a subcritical Hopf bifurcation , or an inverse period ...
The perturbation must be tiny compared to the overall size of the attractor of the system to avoid significant modification of the system's natural dynamics. [2] Several techniques have been devised for chaos control, but most are developments of two basic approaches: the Ott–Grebogi–Yorke (OGY) method and Pyragas continuous control. Both ...
The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions. Chaos theory (or chaology [1]) is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions.
In applied mathematics and astrodynamics, in the theory of dynamical systems, a crisis is the sudden appearance or disappearance of a strange attractor as the parameters of a dynamical system are varied. [1] [2] This global bifurcation occurs when a chaotic attractor comes into contact with an unstable periodic orbit or its stable manifold. [3]
A coupled map lattice (CML) is a dynamical system that models the behavior of nonlinear systems (especially partial differential equations).They are predominantly used to qualitatively study the chaotic dynamics of spatially extended systems.
The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior . The Duffing map takes a point ( x n , y n ) in the plane and maps it to a new point given by