Journal of Vibration Testing and System Dynamics
Dynamical Analysis of a Fractional Order two Species Model of Pest and its Predator
Journal of Vibration Testing and System Dynamics 6(3) (2022) 273296  DOI:10.5890/JVTSD.2022.09.002
Prabir Panja
Department of Applied Science, Haldia Institute of Technology, Haldia721657, West Bengal, India
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Abstract
This paper considers a fractional order two species model incorporating pest and its predator population. It is assumed that the pest population is infected by a disease. Due to this infection, pest population is classified into two sub populations such as susceptible pest and infected pest population. For the biological control of pest species, the predator of pest population is introduced. Here, it is assumed that predator consumes susceptible as well as infected pests. The uniqueness, nonnegativity and boundedness of the solutions of the fractional order system have been studied. Locally asymptotic stability of the equilibrium points has been investigated. Also, global stability of the interior equilibrium point has been analyzed. The existence condition of Hopf bifurcation in the proposed model has been studied. It is found that the stability of the model increases as the value of fractional order derivative $\alpha$ gradually decreases.
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