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Article overview
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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
; | | Date: |
18 May 2015 | | 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. | | Source: | arXiv, 1505.4729 | | Services: | Forum | Review | PDF | Favorites | |
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