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Deterministic and Stochastic Fractional-Order Hastings-Powell Food chain model

Computers, Materials & Continua 2022年第2期70卷 2277-2296页

作者： Moustafa El-Shahed Asmaa M.Al-Dububan Department of Mathematics Unaizah College of Sciences and ArtsQassim UniversityUnaizah51911Saudi Arabia Department of Mathematics Buraydah College of Sciences and ArtsQassim UniversityBuraydah51431Saudi Arabia

In this paper,a deterministic and stochastic fractional-order model of the tri-trophic Food chain model incorporating harvesting is proposed and analysed.The interaction between prey,middle predator and top predator population is investigated.In order to clarify the characteristics of the proposed model,the analysis of existence,uniqueness,non-negativity and boundedness of the solutions of the proposed model are examined.Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained.By using stability analysis of the fractional-order system,it is proved that if the basic reproduction number R_(0)model.

关键词： Food chain model global dynamics stability stochastic Hastings-Powell model harvesting

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Dynamics of an autonomous Food chain model and existence of global attractor of the associated non-autonomous system

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International Journal of Biomathematics 2019年第8期12卷 1-31页

作者： Jyotirmoy Roy Shariful Alam Department of Mathematics Indian Institute of Engineering Science and Technology Shibpur B.GardenHowrah-711103India

In this paper,we have analyzed a tri-trophic Food chain model consisting of phytoplankton,zooplankton and fish population in an aquatic environment.Here,the pelagic water column is divided into two layers namely,the upper layer and the lower layer.The zooplankton population makes a diel vertical migration(DVM)from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator(Fish).Here,mathematical model has been developed and analyzed in a rigorous way.Apart from routine calculations like boundedness and positivity of the solution,local stability of the equilibrium points,we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way.It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system.Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation.The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system,whereas the downward migration rate enhance the stability of the system.FYirther,we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations.We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible.Finally,extensive numerical simulation has been performed to support our analytical findings.

关键词： Food chain model DVM Hopf bifurcation limit cycle periodic solution global attractor

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