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Turing Patterns in a Cross Diffusive System

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Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory (ICRAPAM 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 307))

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Abstract

In this paper we investigate the role of cross diffusion in pattern formation for a tritrophic food chain model. In the formulated model the prey interacts with the mid level predator in accordance with Holling Type II functional response and the mid and top level predator interact via Crowley Martin functional response. We have proved that the stationary uniform solution of the system is stable in the presence of diffusion and absence of cross diffusion but unstable in the presence of cross diffusion. Moreover we carry out numerical simulations to understand the Turing pattern formation for various self and cross diffusivity coefficients of the top level predator.

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Acknowledgements

This work has further been extended and published in [24].

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, 175001, Himachal Pradesh, India

    Nishith Mohan & Nitu Kumari

Authors
  1. Nishith Mohan
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  2. Nitu Kumari
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Corresponding author

Correspondence to Nitu Kumari .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, New Delhi, India

    Naokant Deo

  2. Department of Mathematics, Netaji Subhas University of Technology, New Delhi, India

    Vijay Gupta

  3. Department of Mathematics, Lucian Blaga University of Sibiu, Sibiu, Romania

    Ana Maria Acu

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

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Mohan, N., Kumari, N. (2020). Turing Patterns in a Cross Diffusive System. In: Deo, N., Gupta, V., Acu, A., Agrawal, P. (eds) Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory. ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 307. Springer, Singapore. https://doi.org/10.1007/978-981-15-1157-8_2

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