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Author: search.filters.author.Dubey, BalramSubject: search.filters.subject.Stability

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Now showing 1 - 4 of 4
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    Dynamics of Phytoplankton, Zooplankton and Fishery Resource Model
    (AAM, 2014-06) Dubey, Balram
    In this paper, a new mathematical model has been proposed and analyzed to study the interaction of phytoplankton- zooplankton-fish population in an aquatic environment with Holloing’s types II, III and IV functional responses. It is assumed that the growth rate of phytoplankton depends upon the constant level of nutrient and the fish population is harvested according to CPUE (catch per unit effort) hypothesis. Biological and bionomical equilibrium of the system has been investigated. Using Pontryagin’s Maximum Principal, the optimal harvesting policy is discussed. Chaotic nature and bifurcation analysis of the model system for a control parameter have been observed through a numerical simulation
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    A predator–prey interaction model with self and cross-diffusion
    (Elsevier, 2001-07) Dubey, Balram
    In this paper, a mathematical model for a predator–prey interaction with self and cross-diffusion is proposed and analysed. Criteria for local stability, instability and global stability are obtained. The effect of the critical wave length which can drive a system to instability is investigated. The effect of time-varying cross-diffusivity on the stability of the system is also examined.
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    Modelling the Dynamics of a Renewable Resource under Harvesting with Taxation as a Control Variable
    (AAM, 2014-10) Dubey, Balram
    The present paper describes a model of resource biomass and population with a non-linear catch rate function on resource biomass. The harvesting effort is assumed to be a dynamical variable. Tax on per unit harvested resource biomass is used as a tool to control exploitation of the resource. Pontryagin’s Maximum Principle is used to find the optimal control to maintain the resource biomass and population at an optimal level. A numerical simulation is also carried out to support the analytical results.
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    Stability and Hopf-bifurcation in a general Gauss type two-prey and one-predator system
    (Elsevier, 2016-06) Dubey, Balram
    A Gauss type general prey–predator mathematical model is proposed and analysed to study the effect of predation on two competing prey species. The growth rate and functional responses are taken to be general non-linear functions. By analysing the model, local stability of all possible equilibrium points is discussed. By choosing a suitable Lyapunov function the global stability of the system at positive equilibrium point is also found. For the purpose of numerical simulation, growth rates of both prey species are taken to be logistic and the predator's functional response on the prey species are taken as Holling type-II. Taking death rate of the predator as a bifurcation parameter, we observe Hopf-bifurcation of the system. Then we have discussed the stability and direction of the Hopf-bifurcation. We also observed that intra-specific interference factor is an important parameter in governing the dynamics of the system.