| Abstract: |
| Biological diffusion processes are often influenced by environmental factors. In this talk, we investigate the effects of variable diffusion, which depends on a point between the departure and arrival points, on the propagation of bistable waves. This process includes neutral, repulsive, and attractive transitions. By using singular limit analysis, we derive the equation for the interface between two stable states and examine the relationship between wave propagation and variable diffusion. More precisely, when the transition probability depends on the environment at the dividing point between the departure and arrival points, we derived an expression for the wave propagation speed that includes this dividing point ratio. This shows that, asymptotically, the boundary between wave propagation and blocking in a one-dimensional space corresponds to the case where the transition probability is determined by a dividing point ratio of 3:1 between the departure and arrival points. Furthermore, as an application of this concept, we consider the Aliev-Panfilov model to explore the mechanism for generating target patterns. |
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