Stability analysis for the fractional-order single-species model with the dispersal

摘要

In this paper, the single-species model with the dispersal is extended to the fractional-order model. Caputo fractional order derivatives are used. Fractional-order single-species model with the dispersal is interpreted as a coupled system on a network. By using graph theoretical approach of the coupled systems, constructing Lyapunov functions method and stability theory of the fractional-order system, positive equilibrium's existence theorems and stability theorems for the new model are obtained. An example is given to illustrate the applications of main results.