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arXiv · 1909.02796

Pulsating and rotating spirals in a delayed feedback diffractive nonlinear optical system

Stanislav Budzinskiy·Alexander Razgulin
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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.

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Stanislav Budzinskiy, Alexander Razgulin. 2019-09-06. Pulsating and rotating spirals in a delayed feedback diffractive nonlinear optical system. https://doi.org/10.1142/s0218127421300020

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