Finite-time and exact Lyapunov dimension of the Henon map

Abstract

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.

arXiv commentarXiv admin note: text overlap with arXiv:1504.04723

References in corpus (8)

• Differences and similarities in the analysis of Lorenz, Chen, and Lu systems
• Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
• The Lyapunov dimension and its estimation via the Leonov method
• Existence of perpetual points in nonlinear dynamical systems and its applications
• Hidden transient chaotic attractors of Rabinovich-Fabrikant system
• Hidden attractors on one path: Glukhovsky-Dolzhansky, Lorenz, and Rabinovich systems
• Perpetual points and periodic perpetual loci in maps
• A short survey on Lyapunov dimension for finite dimensional dynamical systems in Euclidean space