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Download as PDF; Printable version ... CM Place, An introduction to dynamical systems, Cambridge University Press, 1990. ... Locking, and Chaos in a Dissipative ...
Chaotic maps often occur in the study of dynamical systems. Chaotic maps and iterated functions often generate fractals . Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them.
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
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.
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 ...
Devaney is known for formulating a simple and widely used definition of chaotic systems, one that does not need advanced concepts such as measure theory. [8] In his 1989 book An Introduction to Chaotic Dynamical Systems, Devaney defined a system to be chaotic if it has sensitive dependence on initial conditions, it is topologically transitive (for any two open sets, some points from one set ...
The Zaslavskii map is a discrete-time dynamical system introduced by George M. Zaslavsky. It is an example of a dynamical system that exhibits chaotic behavior . The Zaslavskii map takes a point ( x n , y n {\displaystyle x_{n},y_{n}} ) in the plane and maps it to a new point:
In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself. It is named after a kneading operation that bakers apply to dough: the dough is cut in half, and the two halves are stacked on one another, and compressed.