A prey-predator model with Holling type IV response function under deterministic and stochastic environment

Dipankar Sadhukhan

Abstract


In this paper, both deterministic and stochastic behaviors of a general prey-predator model have been studied with Holling type-IV response function. For the deterministic model, uniform boundedness and persistence of the system have been discussed under the certain condition of the parameter. For local stability and bifurcation analysis, we arrive at the Hopf bifurcation and derived the symbolic condition for Hopf bifurcation. After that, the model has been illustrated with some numerical examples. In the second phase, the system has been perturbed by independent Gaussian white noises for the stochastic environment and the stability of the system have been studied by statistical linearization technique. Finally, a comparison has been made between the stability conditions in deterministic and stochastic cases.

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Published: 2021-02-23

How to Cite this Article:

Dipankar Sadhukhan, A prey-predator model with Holling type IV response function under deterministic and stochastic environment, Commun. Math. Biol. Neurosci., 2021 (2021), Article ID 18

Copyright © 2021 Dipankar Sadhukhan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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