Chaotic Dynamics in an Integro-Differential Reaction-Diffusion System in the Presence of 0:1:2 Resonance

DOI10.1007/978-4-431-56457-7_19zbMath1366.37093OpenAlexW2559436454MaRDI QIDQ5278263

Takashi Okuda, Toshiyuki Ogawa

Publication date: 13 July 2017

Published in: Mathematical Fluid Dynamics, Present and Future (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-4-431-56457-7_19

zbMATH Keywords

normal formconnecting orbitheteroclinic loop0:1:2 resonance

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Dynamics induced by flows and semiflows (37C10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Cites Work

• Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
• Degenerate Hopf instability in oscillatory reaction-diffusion equations
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry
• Geometric theory of semilinear parabolic equations
• Applications of centre manifold theory
• Singularities and groups in bifurcation theory. Volume II
• The symmetry perspective. From equilibrium to chaos in phase space and physical space
• Oscillatory dynamics in a reaction-diffusion system in the presence of 0:1:2 resonance
• Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction
• The interaction of two spatially resonant patterns in thermal convection. Part 1. Exact 1:2 resonance
• Kuramoto–Sivashinsky Dynamics on the Center–Unstable Manifold
• Chaotic dynamics in ${\mathbb Z}_2$-equivariant unfoldings of codimension three singularities of vector fields in ${\mathbb R}^3$
• New type of complex dynamics in the \(1:2\) spatial resonance

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