2015/11/23 by Rana D. Parshad, Parshad, Rana D., Suman Bhowmick +7
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Analysis of PDEs (math.AP) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #math.AP
paper · pdf · doi:10.48550/arxiv.1511.07498
arxiv created 2015/11/23 · openalex publication_date 2015/11/23 · arxiv updated 2015/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeRK15, we have seen that the model does possess 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 \citeRK15. 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 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.