Work

Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

Year: 2015

Type: article

Abstract: In this paper, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky-Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.

Source: The European Physical Journal Special Topics

DOI: 10.1140/epjst/e2015-02470-3

Authors: G. A. Leonov, N. V. Kuznetsov, T. N. Mokaev

Institutions: St Petersburg University, University of Jyväskylä

Language: English

Topic: Chaos control and synchronization

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,790

Funder: Saint Petersburg State University