### Dynamic Analysis of a Fractional Order Phytoplankton-Zooplankton System with a Crowley-Martin Functional Response

#### Abstract

In this work, we investigate the dynamical behaviour of a fractional order phytoplankton-zooplankton system(PZS) with with a Crowley-Martin functional response. Local stability analysis of biologically feasible equilibrium points is worked out with help of ecological as well as disease basic reproduction numbers. We proved that the equilibrium $E_0=(0,0,0)$ of the PZS is a saddle

point. We proved that the equilibrium $E_1=(\frac{1}{\gamma},0,0)$ of the system is asymptotically stabile if $R_0<1$ and $R_0^*<1$. Also we proved that the equilibrium $E_2=(S_2,I_2,0)$ of the system if $R_0(1)>1$.

Numerical simulations are carried out for a hypothetical set of

parameter values to substantiate our analytical findings.

point. We proved that the equilibrium $E_1=(\frac{1}{\gamma},0,0)$ of the system is asymptotically stabile if $R_0<1$ and $R_0^*<1$. Also we proved that the equilibrium $E_2=(S_2,I_2,0)$ of the system if $R_0(1)>1$.

Numerical simulations are carried out for a hypothetical set of

parameter values to substantiate our analytical findings.

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