In this paper,a diffusive genetic regulatory network under Neumann boundary conditions is considered.First,the criteria for the local stability and diffusion-driven instability of the positive stationary solution with...In this paper,a diffusive genetic regulatory network under Neumann boundary conditions is considered.First,the criteria for the local stability and diffusion-driven instability of the positive stationary solution without and with diffusion are investigated,respectively.Moreover,Turing regions and pattern formation are obtained in the plane of diffusion coeficients.Second,the existence and multiplicity of spatially homogeneous/nonhomogeneous non-constant steady-states are studied by using the Lyapunov-Schmidt reduction.Finally,some numerical simulations are carried out to illustrate the theoretical results.展开更多
基金the National Natural Science Foundation of China(No.12171135)Natural Science Foundation of Hebei Province(Nos.A2019201106 and A2020201021)Post-Graduate's Innovation Fund Project of Hebei University(No.HBU2022bs022).
文摘In this paper,a diffusive genetic regulatory network under Neumann boundary conditions is considered.First,the criteria for the local stability and diffusion-driven instability of the positive stationary solution without and with diffusion are investigated,respectively.Moreover,Turing regions and pattern formation are obtained in the plane of diffusion coeficients.Second,the existence and multiplicity of spatially homogeneous/nonhomogeneous non-constant steady-states are studied by using the Lyapunov-Schmidt reduction.Finally,some numerical simulations are carried out to illustrate the theoretical results.
