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

الموضوعات : فصلنامه ریاضی

A. K. Sharma ¹ ( Department of Mathematics, DAV College Jagraon, India )
A. Sharma ² ( Department of Applied Sciences, DAV Institute of Engineering and Technology, Jalandhar, India )
K. Agnihotri ³ ( Department of Applied Sciences, SBSSTC, Ferozpur, India. )

تاريخ الإرسال : 08 الأربعاء , شوال, 1437 تاريخ التأكيد : 08 الأربعاء , شوال, 1437 تاريخ الإصدار : 26 الجمعة , رمضان, 1437

الکلمات المفتاحية: Turing instability, Zooplankton, Toxin producing phytoplankton, Hopf Bifurcation, Normal Form, Center manifold theorem,

ملخص المقالة :

The present paper deals with a toxin producing phytoplankton (TPP)-zooplankton interaction in spatial environment in thecontext 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 ofHopf bifurcations and the stability of bifurcating periodic solutions is derived. Finally, numericalsimulations supporting the theoretical analysis are also included.

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