Junping Shi
Instability and bifurcation in models with advection, diffusion and delays

In an evolution model, the equilibrium states are the ones which do not depend on time. A constant equilibrium is often stable if the perturbation is also constant one, hence it is dynamically stable with respect to an ODE. More realistic models often include the effect of spatial movement and/or time delays. In this talk, we show that instability of a constant equilibrium can be caused by advection, diffusion, chemotaxis, or time delay. Moreover we show that Hopf bifurcations can occur in many cases so oscillatory states emerge.

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