{
  "id": "1511.07498",
  "version": "v1",
  "published": "2015-11-23T22:44:08.000Z",
  "updated": "2015-11-23T22:44:08.000Z",
  "title": "Finite time Blow up in a population model with competitive interference and time delay",
  "authors": [
    "Rana D. Parshad",
    "Suman Bhowmick",
    "Emmanuel Quansah",
    "Rashmi Agrawal",
    "Ranjit Kumar Upadhyay"
  ],
  "categories": [
    "math.AP"
  ],
  "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 \\cite{RK15}, 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, \\emph{even} under the parametric restrictions derived in \\cite{RK15}. 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-23T22:44:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite time blow",
      "population model",
      "time delay",
      "competitive interference",
      "beddington-deangelis type functional responses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151107498P"
    }
  }
}