Controlling oscillator coherence by multiple delay feedback

Denis S. Goldobin^1, 2 ; Elizaveta V. Shklyaeva²

¹ Institute of Continuous Media Mechanics, Ural Branch of RAS, Perm 614013, Russia.
² Theoretical Physics Department, Perm State University, Perm 614990, Russia.

Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 6.

Résumé

We consider the implementation of a weak feedback with two delay times for controlling the coherence of both deterministic chaotic and stochastic oscillators. This control strategy is revealed to allow one to decrease or enhance the coherence, which is quantified by the phase diffusion constant, by 2–3 orders of magnitude without destruction of the chaotic regime, which is by an order of magnitude more than one can achieve with a single delay time. Within the framework of the phase reduction, which is a rough approximation for the chaotic oscillators and rigorous for the stochastic ones, an analytical theory of the effect is constructed.

Détail

DOI : 10.1051/mmnp/2020049

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