Li Yanling,Ma Yichen
(School of Sciences, Xi'an Jiaotong University, Xi'an 710049, China)
Abstract: Adopting
the comparison principle and the theory of existence, the initial and boundary conditions
of reaction-diffusion systems with time delays are dealt with to obtain the sufficient
conditions for the existence of solutions and global asymptotic stability of a positive
steady-state solution. The result leads to the permanence of the prey-predator systems,
the instability of the trivial and all forms of semitrivial solutions, and the
nonexistence of nonuniform steady-state solutions.
Keywords: reaction-diffusion; time delay; global asymptotic stability; prey-predator
model; comparison principle