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

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Abstract

© 2015, EDP Sciences and Springer.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.
Original languageEnglish
Pages (from-to)1421-1458
JournalEuropean Physical Journal: Special Topics
Issue number8
DOIs
StatePublished - 2015

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