| S.P. Kuznetsov and A.S. Pikovsky We propose several examples of smooth autonomous systems governed by differential delay equation manifesting chaotic dynamics apparently associated with robust hyperbolic attractors. The general idea is to depart from a system generating nesting pulses of oscillations, each of which gives rise to the next one with transformation of the phase in accordance with a chaotic map, like Bernoulli map or Arnold cat map. In contrast to the models considered in our previous papers, these systems are designed on a single active element, which is an obvious advantage from experimental or technical point of view. From mathematical point of view, they are more difficult for description, as relate to a class of infinite-dimensional systems due to presence of the time delay. Nevertheless, the material we present gives a foundation to assert that our models deliver examples of small-dimensional hyperbolic strange attractors, embedded in the infinite-dimensional phase space. |
|