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Global dynamics of stochastic predator–prey model with mutual interference and prey defense

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Abstract

Predator–prey interactions with stochastic forcing have been extensively investigated in the literature. However there are not many investigations of such models, that include prey defense. The goal of the current manuscript is to investigate a stochastic predator–prey model with mutual interference, and various Holling type functional responses, where the prey is able to release toxins as defense against a predator. This can also be generalized to include group or herd defense, toxin production and mimicry. We establish local and global existence for the stochastic model, and perform various numerical simulations to support our theoretical results. Our key result is that we have globally existing solutions independent of the magnitude of the toxin release parameter, or the predation rates. We also show that large enough noise intensity in solely the prey, can lead to extinction in the noisy model, for both species, whilst there is persistence in the deterministic model.

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Acknowledgements

RP would like to acknowledge valuable support from the National Science Foundation via DMS-1715377.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, 826004, India

    Ranjit Kumar Upadhyay & Sarita Kumari

  2. Department of Mathematics, Iowa State University, Ames, IA, 50011, USA

    Rana D. Parshad

  3. Department of Mathematics and Computer Science, Samford University, Birmingham, AL, 35229, USA

    Kwadwo Antwi-Fordjour

  4. PacificSource Health Plans, Springfield, OR, 97477, USA

    Emmanuel Quansah

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  1. Ranjit Kumar Upadhyay
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  2. Rana D. Parshad
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  3. Kwadwo Antwi-Fordjour
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  4. Emmanuel Quansah
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  5. Sarita Kumari
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Correspondence to Ranjit Kumar Upadhyay.

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Upadhyay, R.K., Parshad, R.D., Antwi-Fordjour, K. et al. Global dynamics of stochastic predator–prey model with mutual interference and prey defense. J. Appl. Math. Comput. 60, 169–190 (2019). https://doi.org/10.1007/s12190-018-1207-7

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  • DOI: https://doi.org/10.1007/s12190-018-1207-7

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