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.
Bifurcations in Twinkling Patterns for the Lengyel-Epstein Reaction-Diffusion Model
Sgura I.;
2021-01-01
Abstract
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.File in questo prodotto:
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