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In this tutorial, we discuss self-excited and hidden attractors for systemsof differential equations. We considered the example of a Lorenz-like systemderived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, todemonstrate the analysis of self-excited and hidden attractors and theircharacteristics. We applied the fishing principle to demonstrate the existenceof a homoclinic orbit, proved the dissipativity and completeness of the system,and found absorbing and positively invariant sets. We have shown that thissystem has a self-excited attractor and a hidden attractor for certainparameters. The upper estimates of the Lyapunov dimension of self-excited andhidden attractors were obtained analytically.

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