6533b870fe1ef96bd12d0685
RESEARCH PRODUCT
Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
G. A. LeonovN. V. KuznetsovT. N. Mokaevsubject
Nonlinear Sciences::Chaotic DynamicsMathematics::Dynamical SystemsMaterials Science(all)FOS: Physical sciencesChaotic Dynamics (nlin.CD)Physical and Theoretical ChemistryPhysics and Astronomy(all)Nonlinear Sciences - Chaotic Dynamicsdescription
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.
year | journal | country | edition | language |
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2015-05-18 |