Uniqueness and stability of a predatorprey model with CM functional response ?
In this paper, we are concerned with positive solutions of a predatorprey model with CrowleyMartin functional response under Dirichlet boundary conditions. First, we establish the existence of positive solutions when (a,c) ( a , c ) is close to (?1,?1) ( ? 1 , ? 1 ) . Next, the stability properties of nonnegative solutions are discussed by spectral analysis. In addition, we obtain a complete understanding of the uniqueness and non-uniqueness of positive solutions by the LyapunovSchmidt procedure and the perturbation technique. At last, some numerical simulations are presented to supplement the analytic results in one dimension.
uniqueness stability crowleymartin functional response lyapunovschmidt procedure perturbation technique