An autonomous system with attractor of Smale–Williams type with resonance transfer of excitation in a ring array of van der Pol oscillators

An autonomous system we propose is a ring structure of a large number of van der Pol oscillators, which manifests cyclic propagation of the localized excitation with phase undergoing the expanding circle map transformation on each full revolution. Due to this, it is reasonable to suppose that attractor of Smale–Williams type occurs in the phase space of the system. Because of the slow spatial variation of the natural frequencies of the oscillators around the ring, it appears possible to exploit resonance mechanism for the excitation transfer; so, the system may have prospects for implementation of high-frequency chaos generators.

Research highlights
► An autonomous ring system composed of van der Pol oscillators is suggested as chaos generator.
► Occurrence of Smale-Williams attractor is demonstrated in computations.
► It is expected that devices, based on this model, may be implemented in electronics or optics.