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The Effects of Unequal Diffusion Coefficients on Spatiotemporal Pattern Formation in Prey Harvested Reaction-Diffusion Systems

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Mathematical Analysis and Applications in Modeling (ICMAAM 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 302))

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Abstract

In this investigation, we explore the spatiotemporal dynamics of reaction-diffusion predator-prey systems with Holling type II functional response. For partial differential equation, we consider the diffusion-driven instability of the coexistence equilibrium solution through spatiotemporal patterns. We find the conditions for Turing bifurcation of the system in a two-dimensional spatial domain by making use of the linear stability analysis and the bifurcation analysis. By choosing the ecological system parameter as the bifurcation parameter, we show that the system experiences a sequence of spatiotemporal patterns. The results of numerical simulations unveil that there are various spatial patterns including typical Turing patterns such as hot spots, spots-stripes mixture and stripes pattern through Turing instability. Our results show that the ecological system parameter plays a vital function in the proposed reaction-diffusion predator-prey models. Numerical design has been finally carried out through graphical representations of those outcomes towards the end in order to recognize the spatiotemporal behaviour of the system under study. All the outcomes are predictable to be of use in the study of the dynamic complexity of flora and fauna.

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Acknowledgements

The author confers thank to the anonymous referee for the very helpful ideas and statements which led to developments of our original manuscript. Also, the author gratefully acknowledges the financial support in part from Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India (Grant No. F.510/3/DRS-III/2015 (SAP-I)).

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Authors and Affiliations

  1. Department of Mathematics, Visva-Bharati, Santiniketan, 731235, West Bengal, India

    Lakshmi Narayan Guin

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  1. Lakshmi Narayan Guin
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Correspondence to Lakshmi Narayan Guin .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India

    Priti Kumar Roy

  2. College of Science, Beijing Technology and Business University, Beijing, China

    Xianbing Cao

  3. College of Mathematics and Information Science, Henan Normal University, Xinxiang, Xinjiang, China

    Xue-Zhi Li

  4. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India

    Pratulananda Das

  5. Harish-Chandra Research Institute, Allahabad, Uttar Pradesh, India

    Satya Deo

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Narayan Guin, L. (2020). The Effects of Unequal Diffusion Coefficients on Spatiotemporal Pattern Formation in Prey Harvested Reaction-Diffusion Systems. In: Roy, P., Cao, X., Li, XZ., Das, P., Deo, S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore. https://doi.org/10.1007/978-981-15-0422-8_24

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