The Sprott B system.

Abstract

We will consider a thermostatic system, Sprott B, that is a generalization of the well-known one-parameter Sprott A system. Sprott B contains an explicit periodic solution for all positive values of the parameter a. As for Sprott A, we find dissipative KAM tori associated with time-reversal symmetry and canards in dissipative systems. The exact periodic solution is characterized by an infinite number of instability intervals of the parameter. The investigation of the dynamics in these intervals shows the presence of families of stable and unstable periodic solutions, tori, and strange attractors. For large values of the control parameter a, we find non-hyperbolic slow manifolds producing violent vibrations. We discuss a generalization of the Sprott B system with related dynamics.