A mathematical model is proposed to study a three species food web model of preypredator system in spatiotemporal domain. In this model, we have included three state variables, namely, one prey and two first order predators population with Beddington-DeAngelis predation functional response. We have obtained the local stability conditions for interior equilibrium and the existence of Hopf-bifurcation with respect to the mutual interference of predator as bifurcation parameter for the temporal system. We mainly focus on spatiotemporal system and provided an analytical and numerical explanation for understanding the diffusion driven instability condition. The different types of spatial patterns with respect to different time steps and diffusion coefficients are obtained. Furthermore, the higher-order stability analysis of the spatiotemporal domain is explored.
A mathematical model is proposed to study the role of dissolved oxygen in the plankton ecosystem in spatiotemporal domain, considering one nonliving compartment, i.e., dissolved oxygen and two living compartments, i.e., phytoplankton and zooplankton populations with Holling type II response function for the harvesting rate of phytoplankton by zooplankton population. In temporal system, the local stability analysis of all the feasible equilibria is studied and also explored the existence of Hopf-bifurcation for the interior equilibrium, taking the growth rate of phytoplankton as bifurcation parameter. Further, the direction of Hopf-bifurcation and stability of the bifurcating periodic solutions are presented using normal form theory. In spatial system, we have obtained the condition for diffusion driven instability and obtained different types of spatial patterns with different step size in time. Furthermore, conducted the higher-order stability analysis of the spatiotemporal dynamics. Finally, numerical simulation is given in support of the analytic results for both temporal and spatiotemporal domain.
A mathematical model is proposed and analyzed for the understanding of growth pattern of mosquito vector looking into its life cycle. The objective of this study is to develop a mathematical model that can fit to the real data provided by DRDE scientist for different month at different stations so that the seasonal variation in population density of mosquitoes can be reported accurately to the estimated data obtained by the proposed mathematical model. The aquatic class (L) and adult stage is divided in two class, indoor population (I) and outdoor population (O). Here we estimated different parameters of our proposed continuous model and numerical simulation is done to compare the estimated data with the actual data.
The current study looked into continuous two-dimensional Jeffery fluid flow and heat transfer with radiation and heat source effects past linearly stretched sheet under suction/injection conditions. I have investigated the effects of the magnetic dipole on two different thermal processes: prescribed surface temperature (PST) and prescribed heat flow (PHF). The governing non-linear PDEs are converted into a system of coupled non-linear ODEs using the appropriate transformations, and the numerical solutions are carried out using the bvp4c solver included in the MATLAB package. The effects of the parameters investigated—ferromagnetic interaction parameter (\(\beta\)), Deborah number (\(\gamma\)), radiation parameter (R), heat sources parameter (Q), Prandtl number (Pr), suction/injection parameter (S), ratio of relaxation to retardation times (\({\lambda _2}\)), and Grashof number (Gr)—on velocity and temperature profiles—are graphically depicted in the figures.
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