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Some dynamics in spatial homogeneous and inhomogeneous activator-inhibitor model. (Chinese. English summary) Zbl 1389.35066
Summary: The diffusive Gierer-Meinhardt activator-inhibitor model system with Neumann boundary condition is investigated. For the spatial homogeneous (ODE) system, we perform the asymptotic behavior of the interior equilibrium and the existence and stability of limit cycle surrounding the interior equilibrium. For the spatial inhomogeneous (PDE) system, we consider the Turing instability of the interior equilibrium and show the existence of Turing pattern and inhomogeneous periodic oscillatory pattern. To verify our theoretical results, some numerical simulations are also done as a complement.
35B35 Stability in context of PDEs
35K57 Reaction-diffusion equations
92C15 Developmental biology, pattern formation