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arXiv · 1505.04729

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

G. A. Leonov·N. V. Kuznetsov·T. N. Mokaev
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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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G. A. Leonov, N. V. Kuznetsov, T. N. Mokaev. 2015-05-18. Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion. https://doi.org/10.1140/epjst%2Fe2015-02470-3

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