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Home > Lyapunov fractal

A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour in the a-b plane for a given periodic sequence of as and bs.

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Lyapunov fractalIn mathematics Lyapunov fractals (also known as Markus-Lyapunov fractals are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r periodically switches between two values a and b''. Lyapunov exponentThe Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a measure that determines for each point of phase space, how quickly trajectories that begin in this point diverge over time. Actually, the number of Lyapunov exponents is Lyapunov functionIn the theory of dynamical systems, and control theory, Lyapunov functions named after Aleksandr Mikhailovich Lyapunov, are a family of functions that can be used to demonstrate the stability of some state points of a system. The demonstration of stabilit Lyapunov stabilityLyapunov stability is applicable to only unforced (no control input) dynamical systems. It is used to study the behaviour of dynamical systems under initial perturbations around equilibrium points. Let us consider that the origin is the equilibrium point Lyapunov equationIn control theory, the discrete Lyapunov equation is a system of the form : where is a hermitian matrix. It occurs in many branches of control theory, such as stability analysis and optimal control. This and related equations are named after the Russian m Lyapunov's central limit theoremIn probability theory, Lyapunov's central limit theorem is one of the variants of the central limit theorems. It states that if for each positive integer N we have a set of independent, mean 0 random variables : with : : and :, then : converges in distrib Lyapunov time