Dynamical Analysis of a Fractional Order Delayed Prey-Predator Model With Stage Structure

Abstract

This paper is mainly connected with the investigation of fractional order stage-structured predator-prey system with time delay. By analyzing the corresponding characteristic equations, the local stability of the equilibria is investigated and conditions at which the existence of Hopf bifurcation are derived at positive equilibrium by employing Routh Hurwitz criterion. Both fractional order and time delay are chosen as bifurcation parameters. Further, it is concluded that, if the values of fractional order and time delay exceeds the derived critical value then the solutions of addressed system exhibits oscillatory behavior. Moreover, Lyapunov global stability, complex dynamics of the predator-prey systems are also investigated with or without delay for the incommensurate fractional order. Finally, numerical illustrations are provided to validate the effectiveness of derived analytical results.