Approximating Chaotic Attractors by Period-Three Cycles in Discrete Stochastic Systems

2015/09/01 by Irina Bashkirtseva, Lev Ryashko
Physics and Astronomy · Computer Science · #stochastic dynamics and bifurcation #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation

paper · doi:10.1142/s0218127415501382

Abstract

We study a distribution of random states forced outwards of the general deterministic attractor (regular or chaotic) for one-dimensional discrete-time systems with unimodal map. To approximate this distribution, we replace the original system by the appropriate modeling system with stable 3-cycle and use the stochastic sensitivity function technique. Constructive abilities of the suggested approach are demonstrated in the analysis of noise-induced transitions from chaos to order.

Citations

• Quantitative universality for a class of nonlinear transformations

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