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The European Physical Journal Special Topics

, Volume 224, Issue 8, pp 1421–1458 | Cite as

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
  • G. A. Leonov
  • N. V. Kuznetsov
  • T. N. Mokaev
Open Access
Review
Part of the following topical collections:
  1. Multistability: Uncovering Hidden Attractors

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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Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  • G. A. Leonov
    • 1
  • N. V. Kuznetsov
    • 1
    • 2
  • T. N. Mokaev
    • 1
    • 2
  1. 1.Faculty of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Department of Mathematical Information TechnologyUniversity of JyväskyläJyväskyläFinland

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