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 p...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)<1,the predator free equilibrium point E_(1) is globally asymptotically stable.The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem.Some numerical examples are given to illustrate the theoretical findings.The impact of harvesting on prey and themiddle predator is studied.We conclude that harvesting parameters can control the dynamics of the middle predator.A numerical approximation method is developed for the proposed stochastic fractional-order model.展开更多
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 u...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.展开更多
T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives....T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.展开更多
In this paper a dynamic food chain model for Hong Kong which simulates the transfer of radioactive substances from a fallout deposition via the food chain into the human bodies is built. The model is based on the RADF...In this paper a dynamic food chain model for Hong Kong which simulates the transfer of radioactive substances from a fallout deposition via the food chain into the human bodies is built. The model is based on the RADFOOD model and the BirchallJames algorithm. The radionuclides 13if and 90Sr representing the short-term and long-term risk situations have been studied as sample cases. Various types of crops,and the dietary pattern of the public have been collsidered. The resulting internal radiation doses have been calculated. The results are obtained for food consumption starting at various time after the fallout deposition and for different consumption durations.展开更多
This paper is concerned with an optimal harvesting problem over an infinite horizon for age-dependent n-dimensional food chain model and the analysis of long-term behaviors of the optimal-controlled system. The existe...This paper is concerned with an optimal harvesting problem over an infinite horizon for age-dependent n-dimensional food chain model and the analysis of long-term behaviors of the optimal-controlled system. The existence of overtaking optimal policy is proved and a maximum principle is carefully derived by means of Dubovitskii-Milyutin functional analytical extremum theory. Weak and strong turnpike properties of optimal trajectories are established.展开更多
A dynamic food chain model and program, DYFOM 95, for predicting the radiological consequences of nuclear accident has been developed, which is not only suitable to the West food chain but also to Chinese food chain. ...A dynamic food chain model and program, DYFOM 95, for predicting the radiological consequences of nuclear accident has been developed, which is not only suitable to the West food chain but also to Chinese food chain. The following processes, caused by accident release which will make an impact on radionuclide concentration in the edible parts of vegetable were considered: dry and wet deposition interception and initial retention, translocation, percolation, root uptake and tillage. Activity intake rate of animals, effects of processing and activity intake of human through ingestion pathway ware also considered in calculations. The effects of leaf area index LAI of vegetable were considered in dry deposition model. A method for calculating the contribution of rain with different period and different intensity to total wet deposition was established. The program contains 1 main code and 5 sub codes to calculate dry and wet deposition on surface of vegetable and soil, translocation of nuclides in vegetable, nuclide concentration in the edible parts of vegetable and in animal products and activity intake of human and so on.展开更多
基金The authors gratefully acknowledge Qassim University,represented by the Deanship of Scientific Research,on the financial support under the number(cosao-bs-2019-2-2-I-5469)during the academic year 1440 AH/2019 AD.
文摘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)<1,the predator free equilibrium point E_(1) is globally asymptotically stable.The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem.Some numerical examples are given to illustrate the theoretical findings.The impact of harvesting on prey and themiddle predator is studied.We conclude that harvesting parameters can control the dynamics of the middle predator.A numerical approximation method is developed for the proposed stochastic fractional-order model.
基金Department of Science and Technology(No.DST/Inspire Fellowship/2015/IF150653),Govt,of India.
文摘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.
文摘T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.
文摘In this paper a dynamic food chain model for Hong Kong which simulates the transfer of radioactive substances from a fallout deposition via the food chain into the human bodies is built. The model is based on the RADFOOD model and the BirchallJames algorithm. The radionuclides 13if and 90Sr representing the short-term and long-term risk situations have been studied as sample cases. Various types of crops,and the dietary pattern of the public have been collsidered. The resulting internal radiation doses have been calculated. The results are obtained for food consumption starting at various time after the fallout deposition and for different consumption durations.
基金Acknowledgments This work is supported by the Nature Science Foundation of China （11061017） and the Nature Science Foundation of Gansu Province of China （1010RJZA075）.
文摘This paper is concerned with an optimal harvesting problem over an infinite horizon for age-dependent n-dimensional food chain model and the analysis of long-term behaviors of the optimal-controlled system. The existence of overtaking optimal policy is proved and a maximum principle is carefully derived by means of Dubovitskii-Milyutin functional analytical extremum theory. Weak and strong turnpike properties of optimal trajectories are established.
文摘A dynamic food chain model and program, DYFOM 95, for predicting the radiological consequences of nuclear accident has been developed, which is not only suitable to the West food chain but also to Chinese food chain. The following processes, caused by accident release which will make an impact on radionuclide concentration in the edible parts of vegetable were considered: dry and wet deposition interception and initial retention, translocation, percolation, root uptake and tillage. Activity intake rate of animals, effects of processing and activity intake of human through ingestion pathway ware also considered in calculations. The effects of leaf area index LAI of vegetable were considered in dry deposition model. A method for calculating the contribution of rain with different period and different intensity to total wet deposition was established. The program contains 1 main code and 5 sub codes to calculate dry and wet deposition on surface of vegetable and soil, translocation of nuclides in vegetable, nuclide concentration in the edible parts of vegetable and in animal products and activity intake of human and so on.
