Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
Г. А. ЛеоновFaculty of Mathematics and Mechanics, St. Petersburg State University, St. Petersburg, RussiaН. В. КузнецовDepartment of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, FinlandT. N. MokaevDepartment of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland
2015en
ABI
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.
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