A Ninth-Order Convergent Method for Solving the Steady State Reaction–Diffusion Model

2015 ◽  
Vol 26 (4) ◽  
pp. 593-603
Author(s):  
Akanksha Srivastava ◽  
Manoj Kumar ◽  
Todor Dimitrov Todorov
Keyword(s):  
Steady State ◽  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Convergent Method

scholarly journals The stability of steady-state hot-spot patterns for a reaction-diffusion model of urban crime

2014 ◽  
Vol 19 (5) ◽  
pp. 1373-1410 ◽  
Author(s):  
Theodore Kolokolnikov ◽  
◽  
Michael J. Ward ◽  
Juncheng Wei ◽  
◽  
...  
Keyword(s):  
Steady State ◽  
Diffusion Model ◽  
Hot Spot ◽  
Reaction Diffusion ◽  
Urban Crime ◽  
Reaction Diffusion Model ◽  
The Stability

Bifurcations in Twinkling Patterns for the Lengyel–Epstein Reaction–Diffusion Model

2021 ◽  
Vol 31 (11) ◽  
pp. 2150164
Author(s):  
J. Sarría-González ◽  
Ivonne Sgura ◽  
M. R. Ricard
Keyword(s):  
Steady State ◽  
Hopf Bifurcation ◽  
Diffusion Model ◽  
Reaction System ◽  
Reaction Diffusion ◽  
Spatially Inhomogeneous ◽  
Reaction Diffusion Model ◽  
Spatially Homogeneous ◽  
Time Periodic ◽  
Theoretical Results

Conditions for the emergence of strong Turing–Hopf instabilities in the Lengyel–Epstein CIMA reaction–diffusion model are found. Under these conditions, time periodic spatially inhomogeneous solutions can be induced by diffusive instability of the spatially homogeneous limit cycle emerging at a supercritical Bautin–Hopf bifurcation about the unstable steady state of the reaction system. We report numerical simulations by an Alternating Directions Implicit (ADI) method that show the formation of twinkling patterns for a chosen parameter value, thus confirming our theoretical results.

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