空间齐次和非齐次下活化-抑制模型动力学分析

Abstract

Abstract: 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.

Key words: Reaction-diffusion equations, Limit cycle, Turing instability, Turing pattern, Inhomogeneous periodic oscillatory pattern

CLC Number:

O175.26

Yang Wenbin, Wu Jianhua. Some Dynamics in Spatial Homogeneous and Inhomogeneous Activator-Inhibitor Model[J].Acta mathematica scientia,Series A, 2017, 37(2): 390-400.

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References

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Some Dynamics in Spatial Homogeneous and Inhomogeneous Activator-Inhibitor Model

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