Equilibriums' linear stability of a diffusive model of pioneer and climax species interaction

The linear stability of equilibria for a diffused pioneer and climax species competition model is discussed. This system has at least 4 and at most 6 equilibria with two possible positive equilibria, and thus the dynamical behaviors are very rich. All the constant equilibria of the model are given in the second section, and then the linear stabilities of these equilibria are analyzed in the third section. The sufficient condition or sufficient and necessary condition of the stability for every equilibrium is given. The linearization method is used accompanied with the eigenvalue skill. At the last, an example is given to illustrate the application of the results, with numerical simulation and conclusion discussion are given.