Hopf bifurcation analysis in a one-dimensional Schnakenberg reaction-diffusion model
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Publication:1926172
DOI10.1016/j.nonrwa.2012.01.001zbMath1257.35035OpenAlexW2011644038MaRDI QIDQ1926172
Publication date: 28 December 2012
Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.nonrwa.2012.01.001
Neumann boundary conditionspatially heterogeneous periodic solutionspatially homogeneous periodic solution
Periodic solutions to PDEs (35B10) Bifurcations in context of PDEs (35B32) Semilinear parabolic equations (35K58) Initial-boundary value problems for second-order parabolic systems (35K51)
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Cites Work
- Unnamed Item
- Bifurcations of patterned solutions in the diffusive Lengyel-Epstein system of CIMA chemical reactions
- Steady-state solution for a general Schnakenberg model
- Stability and bifurcation in two species predator-prey models
- Turing pattern formation for reaction-convection-diffusion systems in fixed domains submitted to toroidal velocity fields
- Flow-distributed spikes for Schnakenberg kinetics
- Spatiotemporal pattern formation and multiple bifurcations in a diffusive bimolecular model
- Stationary multiple spots for reaction-diffusion systems
- Hopf bifurcation analysis in the 1-D Lengyel-Epstein reaction-diffusion model
- Multiscale analysis for diffusion-driven neutrally stable states
- Transitions and heteroclinic cycles in the general Gierer-Meinhardt equation and cardiovascular calcification model
- Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system
- Hopf bifurcation analysis of a reaction-diffusion Sel'kov system
- Turing instabilities at Hopf bifurcation
- Nonconstant positive steady states for a ratio-dependent predator-prey system with cross-diffusion
- Spatio-temporal pattern formation on spherical surfaces: numerical simulation and application to solid tumour growth
- Stability analysis of Turing patterns generated by the Schnakenberg model
- Weakly nonlinear stability analyses of one-dimensional Turing pattern formation in activator-inhibitor/immobilizer model systems
- Spot self-replication and dynamics for the Schnakenburg model in a two-dimensional domain
- MULTIPLE BIFURCATION ANALYSIS AND SPATIOTEMPORAL PATTERNS IN A 1-D GIERER–MEINHARDT MODEL OF MORPHOGENESIS
- Dynamical transitions of Turing patterns
- The chemical basis of morphogenesis
- Semistrong Pulse Interactions in a Class of Coupled Reaction-Diffusion Equations
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