SPATIOTEMPORAL DYNAMIC OF TOXIN PRODUCING PHYTOPLANKTON (TPP)-ZOOPLANKTON INTERACTION

International Journal of Mathematical Modelling & Computations

مقاله 1، دوره 6، 3 (SUMMER)، مهر 2016، صفحه 189-197   

نویسندگان

A. K. Sharma¹؛ A. Sharma^{* 2}؛ K. Agnihotri³

¹Department of Mathematics, DAV College Jagraon, India

²Department of Applied Sciences, DAV Institute of Engineering and Technology, Jalandhar, India

³Department of Applied Sciences, SBSSTC, Ferozpur, India.

چکیده

The present paper deals with a toxin producing phytoplankton (TPP)-zooplankton interaction in spatial environment in the
context of phytoplankton bloom. In the absence of diffusion the stability of the given system in terms of co-existence and hopf bifurcation has been discussed. After that TPP-zooplankton interaction is considered in spatiotemporal domain by assuming self diffusion in both population. It has been obtained that in the presence of diffusion given system becomes unstable (Turing instability) under certain conditions. Moreover, by applying the normal form theory and the center manifold reduction for partial differential equations (PDEs), the explicit algorithm determining the direction of
Hopf bifurcations and the stability of bifurcating periodic solutions is derived. Finally, numerical
simulations supporting the theoretical analysis are also included.

کلیدواژه‌ها

Toxin producing phytoplankton؛ Zooplankton؛ Hopf Bifurcation؛ Turing instability؛ Normal Form؛ Center manifold theorem

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