{
  "id": "2104.09166",
  "version": "v1",
  "published": "2021-04-19T09:42:25.000Z",
  "updated": "2021-04-19T09:42:25.000Z",
  "title": "Effect of Delay and Control on a Predator-prey Ecosystem with Hassell-Varley Functional Response of Generalist Predator",
  "authors": [
    "Rajesh Ranjan Patra",
    "Soumen Kundu",
    "Sarit Maitra"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Generalist predators are an important component of an ecosystem which may act as a biocontrol agent and influence the dynamics significantly. In this paper, we have studied the effect of delayed logistic growth of the prey species with Hassell-Varley functional response of generalist predator. The Lyapunov stability criteria for the interior equilibrium point is derived. Conditions for alternative stable solutions are obtained using the Kolmogorov theorem and hence we get a stable system. Also, the condition of Hopf-bifurcation and the point of bifurcation are obtained. The length of the delay is also estimated for the system to preserve stability. Numerical simulations are performed and illustrated to support the obtained analytical results. It is observed that by the application of an indirect feedback control mechanism, the system can be brought back to a stable state which was earlier unstable. Latin Hypercube Sampling/Partial Rank Correlation Coefficient (LHS/PRCC) sensitivity analysis, which is an efficient tool often employed in uncertainty analysis, is used to explore the entire parameter space of a model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-19T09:42:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hassell-varley functional response",
      "generalist predator",
      "predator-prey ecosystem",
      "hypercube sampling/partial rank correlation coefficient",
      "latin hypercube sampling/partial rank correlation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}