Stochastic representation of chaos using terminal attractors
نویسنده
چکیده
A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence. 2004 Elsevier Ltd. All rights reserved.
منابع مشابه
Sensitivity analysis of stochastic attractors and noise-induced transitions for population model with Allee effect.
We study a stochastically forced predator-prey model with Allee effect. In the deterministic case, this model exhibits non-trivial stable equilibrium or limit cycle corresponding to the coexistence of both species. Computational methods based on the stochastic sensitivity functions technique are suggested for the analysis of the dispersion of random states in stochastic attractors. Our method a...
متن کاملStochastic multiresonance in the coupled relaxation oscillators.
We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh-Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have dif...
متن کاملDynamical behavior and synchronization of chaotic chemical reactors model
In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of proposed method is proved by Barbalate’s lemma. Numeri...
متن کاملDiscrete Iterated Function Systems
discrete iterated function systems discrete iterated function systems representation of discrete sequences with dimensional discrete iterated function systems discrete iterated function systems stochastic discrete scale invariance: renormalization representation of discrete sequences with high-dimensional power domains and iterated function systems fractal tilings from iterated function systems...
متن کاملA useful canonical form for low dimensional attractors
Powerful computational techniques have been developed to study chaotic attractors that are generated by stretching and folding processes. These include relative rotation rates for determining the organization of unstable periodic orbits and simplex distortion procedures for estimating the topological entropy of these orbits. These methods are useful for attractors contained in a genus-one torus...
متن کامل