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