The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coeffic...The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coefficient D = 0 and the solution blows up ifD= 0. The method of linearization is applied to derive the existence of Hopfs bifurcation which is the signature of instability of Turing system. The increasing of the size of the attractor and the existence of Hopf＇ s bifurcation indicate that there is a threshold that initiates the instability.展开更多
文摘The generalized maximum principle of Lou and Ni is extended from elliptic equations to parabolic equations. By this result, one can show that the system of fugal mycelia has a global attractor if the diffusion coefficient D = 0 and the solution blows up ifD= 0. The method of linearization is applied to derive the existence of Hopfs bifurcation which is the signature of instability of Turing system. The increasing of the size of the attractor and the existence of Hopf＇ s bifurcation indicate that there is a threshold that initiates the instability.
