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math-ph2005
Excitability in a Model with a Saddle-Node Homoclinic Bifurcation
Rui Dilao, Andras Volford
In order to describe excitable reaction-diffusion systems, we derive a two-dimensional model with a Hopf and a semilocal saddle-node homoclinic bifurcation. This model gives the th…
math-ph2005
Turing Instabilities and Patterns Near a Hopf Bifurcation
Rui Dilao
We derive a necessary and sufficient condition for Turing instabilities to occur in two-component systems of reaction-diffusion equations with Neumann boundary conditions. We apply…