Bifurcation analysis of nonlinear reaction-diffusion equations. II: Steady state solutions and comparison with numerical simulations
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Publication:1224959
DOI10.1007/BF02459527zbMath0324.92004MaRDI QIDQ1224959
Publication date: 1975
Published in: Bulletin of Mathematical Biology (Search for Journal in Brave)
Stabilization of systems by feedback (93D15) Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) General biology and biomathematics (92B05)
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Cites Work
- Unnamed Item
- The bifurcation diagram of a model chemical reaction - II. Two dimensional time-periodic patterns
- Patterns of phase compromise in biological cycles
- Topics in stability and bifurcation theory
- Dissipative Structures, Catastrophes, and Pattern Formation: A Bifurcation Analysis
- Plane Wave Solutions to Reaction-Diffusion Equations
- The chemical basis of morphogenesis
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