Control of wavefront propagation in bistable delayed-feedback oscillators

Abstract

As discussed and proved in various studies, delay-feedback oscillators can phenomenologically describe ensembles of locally coupled oscillators. Following this concept, one can expect the occurrence of the effect of deterministic and stochastic wavefront propagation in a single bistable delayed-feedback oscillator, which was reported repeatedly. Moreover, it can be expected that wavefront propagation control schemes successfully applied on examples of ensembles can be similarly realized in delayed-feedback oscillators, which is discussed in the present talk. In particular, two approaches, varying the parameters of external noise and coupling several delayed-feedback oscillators are shown to be promising strategies. First, it has been established that additive Lévy noise induces wavefront propagation in a bistable delayed-feedback oscillator assumed to be symmetric such that its dynamics replicates the collective behaviour in the ensemble with unidirectional local coupling. The wavefront propagation velocity used in this analysis is shown to be varied when adjusting the noise parameters. In addition, it is demonstrated that coupled bistable delayed-feedback oscillators emulate a multilayer network, where one single-layer network is connected to another single-layer network through coupling between replica nodes, i.e. the multiplex network. It is shown that all the aspects of the multiplexing impact on wavefront propagation identified in multilayer networks of bistable oscillators are entirely reproduced in the dynamics of time-delay oscillators. The numerical exploration of the delayed-feedback oscillators is complemented by physical experiments, showing a good correspondence.

This work was supported by the Russian Science Foundation (project No. 24-72-00054).
https://rscf.ru/project/24-72-00054/

Speaker

Vladimir Semenov
Saratov State University
Russia

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