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

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.

submitted to EPJ

References in corpus (3)

• Differences and similarities in the analysis of Lorenz, Chen, and Lu systems
• Existence of perpetual points in nonlinear dynamical systems and its applications
• Estimation of Lyapunov dimension for the Chen and Lu systems