https://doi.org/10.1140/epjst/e2015-02470-3
Review
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
Homoclinic orbits, and self-excited and hidden attractors
1 Faculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, Russia
2 Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland
a e-mail: nkuznetsov239@gmail.com
Received: 17 March 2015
Revised: 20 May 2015
Published online: 27 July 2015
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.
© EDP Sciences, Springer-Verlag, 2015
