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Pulsating and Rotating Spirals in a Delayed Feedback Diffractive Nonlinear Optical System

Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory 1/52, Moscow 119991, Russia

E-mail Address: stanislav.budzinskiy@protonmail.ch

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Alexander Razgulin

Faculty of Computational Mathematics and Cybernetics, Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, Leninskie Gory 1/52, Moscow 119991, Russia

E-mail Address: razgulin@cs.msu.ru

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https://doi.org/10.1142/S0218127421300020Cited by:2 (Source: Crossref)

Abstract

We study spiral waves in a mathematical model of a nonlinear optical system with a feedback loop. Starting from a delayed scalar diffusion equation in a thin annulus with oblique derivative boundary conditions, we shrink the annulus and derive the limiting equation on a circle. Based on the explicitly constructed normal form of the Hopf bifurcation for the one-dimensional delayed scalar diffusion equation, we make predictions about the existence and stability of two-dimensional spirals that we verify in direct numerical simulations, observing pulsating and rotating spiral waves.

Keywords:

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