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Mutual interference and prey refuge are important drivers of predator-preydynamics. The "exponent" or degree of mutual interference has been under muchdebate in theoretical ecology. In the present work, we investigate theinterplay of the mutual interference exponent, on the behavior of apredator-prey model with a generalized Holling type functional response. Weinvestigate stability properties of the system and derive conditions for theoccurrence of saddle-node and Hopf-bifurcations. A sufficient condition forextinction of the prey species has also been derived for the model. Inaddition, we investigate the effect of a prey refuge on the population dynamicsof the model and derive conditions for the prey refuge that would yieldpersistence of populations. We provide additional verification our analyticalresults via numerical simulations. Our findings are in accordance withclassical experimental results in ecology by Gauss G. F (1934), that show thatextinction of predator and prey populations is possible in a finite time period- but that bringing in refuge can effectively cause persistence.

Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference