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- Title
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion.
- Authors
Leonov, G.; Kuznetsov, N.; Mokaev, T.
- 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.
- Publication
European Physical Journal: Special Topics, 2015, Vol 224, Issue 8, p1421
- ISSN
1951-6355
- Publication type
Article
- DOI
10.1140/epjst/e2015-02470-3