Embedding the dynamics of a single delay system into a feed-forward ring

Klinshov, Vladimir, Shchapin, Dmitry, Yanchuk, Serhiy, Wolfrum, Matthias, D'Huys, Otti and Neokorkin, Vladimir (2017). Embedding the dynamics of a single delay system into a feed-forward ring. Physical Review E, 96 (4),

Abstract

We investigate the relation between the dynamics of a single oscillator with delayed self-feedback and a feed-forward ring of such oscillators, where each unit is coupled to its next neighbor in the same way as in the self-feedback case. We show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring. In particular, if for the single oscillator the periodic solution is resonant to the delay, it can be embedded into a ring with instantaneous couplings. We discover several cases where the stability of a periodic solution for the single unit can be related to the stability of the corresponding rotating wave in the ring. As a specific example we demonstrate how the complex bifurcation scenario of simultaneously emerging multi-jittering solutions can be transferred from a single oscillator with delayed pulse feedback to multi-jittering rotating waves in a sufficiently large ring of oscillators with instantaneous pulse coupling. Finally, we present an experimental realization of this dynamical phenomenon in a system of coupled electronic circuits of FitzHugh-Nagumo type.

Publication DOI: https://doi.org/10.1103/PhysRevE.96.042217
Divisions: Engineering & Applied Sciences
Additional Information: Copyright: American Physical Society. Funding: Russian Scientific Foundation (project 16-42-01043 for the Institute of Applied Physics) and the German Research Foundation (project SCHO 307/15-1 and YA 225/3-1 for TU Berlin).
Uncontrolled Keywords: coupled oscillators,delay systems
Published Date: 2017-10-27
Authors: Klinshov, Vladimir
Shchapin, Dmitry
Yanchuk, Serhiy
Wolfrum, Matthias
D'Huys, Otti ( 0000-0001-7498-6771)
Neokorkin, Vladimir

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