Local Dynamics of the Two-Component Singular Perturbed Systems of Parabolic Type

DOI10.1142/S0218127415501424zbMath1327.35010OpenAlexW2204557425MaRDI QIDQ3457736

Ilya S. Kaschenko, Sergey A. Kaschenko

Publication date: 17 December 2015

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127415501424

zbMATH Keywords

nonlinear dynamicsparabolic equationsquasi-normal forms

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Geometric theory, characteristics, transformations in context of PDEs (35A30) Bifurcations in context of PDEs (35B32) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (7)

Local dynamics of two-component parabolic systems of Schrödinger type ⋮ Slow and fast oscillations in a model of an optoelectronic oscillator with delay ⋮ Relaxation modes of a system of diffusion coupled oscillators with delay ⋮ Families of normalizes equations in the problem of dislocations in a solid body ⋮ Regular and irregular solutions in the problem of dislocations in solids ⋮ Local solutions of the fast-slow model of an optoelectronic oscillator with delay ⋮ Rectangular structures in the model of an optoelectronic oscillator with delay

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multistability in nonlinear parabolic systems with low diffusion
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Complex ordering and stochastic oscillations in a class of reaction- diffusion systems with small diffusion
• Quasi-normal forms of two-component singularly perturbed systems
• Travelling wave dynamics in a nonlinear interferometer with spatial field transformer in feedback
• Quasi-normal forms for parabolic systems with strong nonlinearity and weak diffusion
• Parametric transverse patterns in broad aperture lasers
• NORMALIZATION IN THE SYSTEMS WITH SMALL DIFFUSION
• BIFURCATIONAL FEATURES IN SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS WITH WEAK DIFFUSION
• Ordinary Differential Equations

This page was built for publication: Local Dynamics of the Two-Component Singular Perturbed Systems of Parabolic Type