6533b829fe1ef96bd1289b56

RESEARCH PRODUCT

Finite-time and exact Lyapunov dimension of the Henon map

N. V. KuznetsovG. A. LeonovT. N. Mokaev

subject

Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical SystemsFOS: Physical sciencesChaotic Dynamics (nlin.CD)Nonlinear Sciences - Chaotic Dynamics

description

This work is devoted to further consideration of the Henon map with negative values of the shrinking parameter and the study of transient oscillations, multistability, and possible existence of hidden attractors. The computation of the finite-time Lyapunov exponents by different algorithms is discussed. A new adaptive algorithm for the finite-time Lyapunov dimension computation in studying the dynamics of dimension is used. Analytical estimates of the Lyapunov dimension using the localization of attractors are given. A proof of the conjecture on the Lyapunov dimension of self-excited attractors and derivation of the exact Lyapunov dimension formula are revisited.

yearjournalcountryeditionlanguage
2017-12-03
http://arxiv.org/abs/1712.01270