Time Dependent Diffusion Coefficient

Various population dynamic models are being developed to describe the dynamics of a simple predator-prey system. The lowest level of food chain in a water habitat is the producer (Algae) and grazer (Daphnia) interaction. The behaviour of planktons in an interactive environment can be described by reaction-diffusion dynamic model. The diffusion part of the model governs the mass transport of species by diffusion. In many population dynamics models, the diffusion coeffcient of planktons are considered as a constant. Our work shows that the diffusion coefficient of zooplankton (Daphnia) depends on time. It behaves linearly with time. Further, this study is extended to investigate the behavior of diffusion coefficient under spatially heterogeneous environment using the FokkerPlanck equation with probability density function of behavior of zooplankton.

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