Stability, bifurcation and control of a predator-prey ecosystem with prey herd behaviour against generalist predator with gestation delay

In this paper, we proposed a population model depicting the dynamics of a prey species showing group defence against a generalist predator. The group defence characteristic is represented by a non-monotonic functional response. We have established the local stability of the model around the co-existent equilibrium solution using a local Lyapunov function. Condition for existence Hopf bifurcation is obtained along with its normal form. Numerical simulations have been done to confirm the obtained analytical results as well as to validate the proposed model. Sensitivity analysis of the parameters is performed using Latin hypercube sampling(LHS)/partial rank correlation coefficient(PRCC). Blow-up in the population is controlled using the Z-type dynamic method.

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