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Mathematical modeling and analysis of spatial-temporal populationdistributions of interacting species have gained significant attention inbiology and ecology in recent times. In this work, we investigate aBazykin-type prey-predator model with a non-monotonic functional response toaccount for the group defense among the prey population. Various local andglobal bifurcations are identified in the temporal model. Depending on theparameter values and initial conditions, the temporal model can exhibit longstationary or oscillatory transient states due to the presence of a localsaddle-node bifurcation or a global saddle-node bifurcation of limit cycles,respectively. We further incorporate the movement of the populations consistingof a diffusive flux modelling random motion and an advective flux modellinggroup defense-induced prey-taxis of the predator population. The globalexistence and boundedness of the spatio-temporal solutions are establishedusing $L^p$-$L^q$ estimate. We also demonstrate the existence of anon-homogeneous stationary solution near the Turing thresholds using weaklynonlinear analysis. A few interesting phenomena, which include extinctioninside the Turing region, long stationary transient state, and non-homogeneousoscillatory solutions inside the Hopf region, are also identified.

Spatio-temporal dynamics in a diffusive Bazykin model: effects of group defense and prey-taxis