1. Finite Time Blow-up in a Delayed Diffusive Population Model with Competitive Interference.
- Author
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Parshad, Rana D., Bhowmick, Suman, Quansah, Emmanuel, Agrawal, Rashmi, and Upadhyay, Ranjit Kumar
- Subjects
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DELAY differential equations , *HOPF bifurcations , *COMPUTER simulation , *LOTKA-Volterra equations , *FUNCTIONAL differential equations - Abstract
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 blowup. 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. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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