Homoclinic Bifurcations of the Merging Strange Attractors in the Lorenz-like System

2018/02/21 by Г. А. Леонов, Leonov, G. A., R. N. Mokaev +5
Physics and Astronomy · Computer Science · #Chaos control and synchronization #Quantum chaos and dynamical systems #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.1802.07694

Abstract

In this article we construct the parameter region where the existence of a homoclinic orbit to a zero equilibrium state of saddle type in the Lorenz-like system will be analytically proved in the case of a nonnegative saddle value. Then, for a qualitative description of the different types of homoclinic bifurcations, a numerical analysis of the detected parameter region is carried out to discover several new interesting bifurcation scenarios.

Related

• Analytically tractable reconstruction of singular hyperbolic and quasi-strange attractors of Lorenz-type systems
• Appearance of discrete Lorenz attractors in the transitions from saddle to saddle-focus
• Bifurcations and strange attractors
• Analytic proof of the existence of the Lorenz attractor in the extended Lorenz model
• A bifurcational geometric approach to the problem of chaos transition in the classical Lorenz system