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In the current manuscript, an attempt has been made to understand the dynamics of a time-delayed predator-prey system with modified Leslie-Gower and Beddington-DeAngelis type functional responses for large initial data. In Ref. Upadhyay and Agrawal, 83(2016) 821–837, it was shown that the model possesses globally bounded solutions, for small initial conditions, under certain parametric restrictions. Here, we show that actually solutions to this model system can blow-up in finite time, for large initial condition,  even  under the parametric restrictions derived in Ref. Upadhyay and Agrawal, 83(2016) 821–837. We prove blow-up in the delayed model, as well as the non-delayed model, providing sufficient conditions on the largeness of data, required for finite time blow-up. Numerical simulations show that actually the initial data does not have to be very large, to induce blow-up. The spatially explicit system is seen to possess non-Turing instability. We have also studied Hopf-bifurcation direction in the spatial system, as well as stability of the spatial Hopf-bifurcation using the central manifold theorem and normal form theory.

Finite Time Blow-up in a Delayed Diffusive Population Model with Competitive Interference