Turing-Hopf bifurcation in the reaction-diffusion equations and its applications
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Publication:2199577
DOI10.1016/j.cnsns.2015.10.002OpenAlexW1929947366MaRDI QIDQ2199577
Yongli Song, Tonghua Zhang, Yahong Peng
Publication date: 11 September 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.2015.10.002
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Cites Work
- Unnamed Item
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- Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions
- Hopf bifurcation and steady-state bifurcation for an autocatalysis reaction-diffusion model
- Stability and Hopf bifurcation in a diffusive predator-prey system with delay effect
- Dynamics and pattern formation in a diffusive predator-prey system with strong Allee effect in prey
- Spatiotemporal pattern formation and multiple bifurcations in a diffusive bimolecular model
- Order reduction of retarded nonlinear systems - the method of multiple scales versus center-manifold reduction
- Bogdanov-Takens singularity in Van der Pol's oscillator with delayed feedback
- Approximate inertial manifolds for reaction-diffusion equations in high space dimension
- Diffusion-driven instability and bifurcation in the Lengyel-Epstein system
- Hopf bifurcation analysis in the 1-D Lengyel-Epstein reaction-diffusion model
- Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
- Hopf bifurcation analysis of a reaction-diffusion Sel'kov system
- On steady-state solutions of the Brusselator-type system
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Inertial manifolds for nonlinear evolutionary equations
- Applications of centre manifold theory
- Ordinary differential equations (ODE's) on inertial manifolds for reaction-diffusion systems in a singularly perturbed domain with several thin channels
- Elements of applied bifurcation theory.
- Finite-dimensional control of parabolic PDE systems using approximate inertial manifolds
- Creation of spatial structure by an electric field applied to an ionic cubic autocatalator system
- Bogdanov-Takens bifurcation in an oscillator with negative damping and delayed position feedback
- Non-constant positive steady states of the Sel'kov model.
- Computing inertial manifolds
- Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
- Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
- The effect of delay on a diffusive predator-prey system with Holling type-II predator functional response
- Amplitude equations for reaction-diffusion systems with a Hopf bifurcation and slow real modes
- Bifurcation analysis of a diffusive ratio-dependent predator-prey model
- Spatiotemporal dynamics in a diffusive ratio-dependent predator-prey model near a Hopf-Turing bifurcation point
- Bifurcation analysis of reaction-diffusion Schnakenberg model
- Singularity analysis on a planar system with multiple delays
- Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects
- Non-constant steady-state solutions for Brusselator type systems
- Zero singularities of codimension two and three in delay differential equations
- Inertial Manifolds for Reaction Diffusion Equations in Higher Space Dimensions
- Centre manifolds for partial differential equations with delays
- STEADY-STATE, HOPF AND STEADY-STATE-HOPF BIFURCATIONS IN DELAY DIFFERENTIAL EQUATIONS WITH APPLICATIONS TO A DAMPED HARMONIC OSCILLATOR WITH DELAY FEEDBACK
- Hopf bifurcation and Turing instability in the reaction-diffusion Holling-Tanner predator-prey model
- Normal forms and Hopf bifurcation for partial differential equations with delays
- Inertial manifolds and finite-dimensional reduction for dissipative PDEs
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