Bifurcation analysis of nonlinear reaction-diffusion equations—II. Steady state solutions and comparison with numerical simulations

1975 ◽  
Vol 37 (6) ◽  
pp. 589-636 ◽  
Author(s):  
M. Herschkowitz-Kaufman
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Nonlinear Reaction ◽  
Steady State Solutions

Steady State Bifurcation and Patterns of Reaction–Diffusion Equations

2020 ◽  
Vol 30 (11) ◽  
pp. 2050215
Author(s):  
Chunrui Zhang ◽  
Baodong Zheng
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Spatial Region ◽  
Bifurcation Points ◽  
Steady State Bifurcation ◽  
Theoretical Results

In this paper, steady state bifurcations arising from the reaction–diffusion equations are investigated. Using the Lyapunov–Schmidt reduction on a square domain, a simple, and a double steady state bifurcation caused by the symmetry of spatial region is obtained. By examining the reduced bifurcation equations, complete bifurcation scenario and patterns at simple and double steady state bifurcation points are obtained. Numerical simulations support the theoretical results.

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