Hopf bifurcation in diffusive model of nonlinear optical system with matrix Fourier filtering

DOI10.1016/J.CNSNS.2019.04.028zbMath1478.78064OpenAlexW2942592673WikidataQ127935755 ScholiaQ127935755MaRDI QIDQ2206570

Sofia V. Sazonova, A. V. Razgulin

Publication date: 22 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2019.04.028

zbMATH Keywords

Hopf bifurcationrotating wavefunctional-differential diffusion equationFourier filteringnonlinear optical system

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Periodic solutions to PDEs (35B10) Partial functional-differential equations (35R10) Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Lasers, masers, optical bistability, nonlinear optics (78A60) Bifurcations in context of PDEs (35B32)

Related Items (2)

Optimization of the matrix Fourier-filter for a class of nonlinear optical models with an integral objective functional ⋮ Limit cycles bifurcating of Kolmogorov systems in \(\mathbb{R}^2\) and in \(\mathbb{R}^3\)

Cites Work

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• Bifurcation theory. An introduction with applications to partial differential equations
• Projection--difference method for controlled Fourier filtering
• Hopf bifurcation for fully nonlinear equations in Banach space
• Infinite matrices of operators
• Geometric theory of semilinear parabolic equations
• The Hopf bifurcation theorem in infinite dimensions
• Rotating spiral waves in a nonlinear optical system with spatial interactions
• Reducing dimensionality to model 2D rotating and standing waves in a delayed nonlinear optical system with thin annulus aperture
• On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback
• Perturbation theory for linear operators.
• The symmetry perspective. From equilibrium to chaos in phase space and physical space
• On a model of amplitude-phase filtering in a nonlinear optical system with feedback
• Rotating and standing waves in a diffractive nonlinear optical system with delayed feedback under \(O(2)\) Hopf bifurcation
• Two-dimensional rotating waves in a functional-differential diffusion equation with rotation of spatial arguments and time delay
• Rotating structures in a parabolic functional-differential equation
• Rotating waves in parabolic functional differential equations with rotation of spatial argument and time delay
• Boundary-value problems for elliptic functional-differential equations and their applications
• Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics
• Fourier Optics in Image Processing

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