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

2015/05/18 by G. A. Leonov, N. V. Kuznetsov, T. N. Mokaev · 1 citation
Physics and Astronomy · #nlin.CD

paper · pdf · doi:10.1140/epjst/e2015-02470-3

published as Eur. Phys. J. Special Topics 224, 1421-1458 (2015) · submitted to EPJ

arxiv created 2015/05/18 · arxiv updated 2015/07/20

Abstract

In this tutorial, 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.

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• Lyapunov dimension formula for the global attractor of the Lorenz system

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