By means of the continuation theorem of the coincidence degree theory,the existence of two periodic solutions of a delayed single species model with feedback regulation and harvest term is obtained.
This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions fo...This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established.展开更多
We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence de...We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least four positive periodic solutions of this model.展开更多
A class of oscillator of the EI Nifio-Southern oscillation model is considered. Using Mawhin＇s continuation theorem, a result on the existence of periodic solutions for ENSO model is obtained.
In this paper, the existence of two positive periodic solutions for a generalized delayed population model with an exploited term is established by using the continuation theorem of the coincidence degree theory.
With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomou...With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.展开更多
By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r &l...By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.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
In this paper, we study a non-autonomous ratio-dependent predator-prey model with exploited term. By means of the coincidence degree theory, we establish a sufficient condition for the existence of at least two positi...In this paper, we study a non-autonomous ratio-dependent predator-prey model with exploited term. By means of the coincidence degree theory, we establish a sufficient condition for the existence of at least two positive periodic solutions of this model.展开更多
By means of the theory of coincidence degree, sufficient condition for the existence of positive periodic solution to certain neutral delay competition model is obtained.
In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence ...In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.展开更多
In this paper, we study a non-autonomous ratio-dependent predator-prey model with predator＇s harvest. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least two po...In this paper, we study a non-autonomous ratio-dependent predator-prey model with predator＇s harvest. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least two positive periodic solutions of this model.展开更多
Discrete-time analogue of mutualism model is introduced. The discrete-time analogues is considered to be numerical discretization of the continuous-time models and we study their dynamical characteristics. It is shown...Discrete-time analogue of mutualism model is introduced. The discrete-time analogues is considered to be numerical discretization of the continuous-time models and we study their dynamical characteristics. It is shown that the discrete-time analogues preserve the periodicity of the continuous-time models.展开更多
In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solution of a mutualism system with infinite delays. Our results generalize thos...In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solution of a mutualism system with infinite delays. Our results generalize those of Yang etc. [8] and Gopalsamy and He [7].展开更多
By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1...By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1.2,3,4), Di(t) (i = 1,2), a12(t), a21(t), a23(t) and a32(t) are all positive periodic continuous functions with period w > 0, Ti(i = 1,2) are positive constants.展开更多
The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By m...The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.展开更多
In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient c...In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.展开更多
基金Supported by the Science and Technical Foundation to Hubei University of Technology[2006(5)]
文摘By means of the continuation theorem of the coincidence degree theory,the existence of two periodic solutions of a delayed single species model with feedback regulation and harvest term is obtained.
文摘This paper considers a class of ratio-dependent Holling-Taner model with infinite delay and prey harvest, which is of periodic coefficients. By means of the coincidence degree theory, a set of sufficient conditions for the existence of at least two positive periodic solutions of this model is established.
基金Supported by the China Postdoctoral Science Foundation (20060400267)
文摘We study a non-autonomous ratio-dependent predator-prey model with exploited terms. This model is of periodic coefficients, which incorporates the periodicity of the varying environment. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least four positive periodic solutions of this model.
基金Project supported by the National Natural Science Foundation of China (Grant No. 40676016)the Natural Science Foundationof Jiangsu Province of China (Grant Nos. BK2009105 and BK2008119)+2 种基金the Natural Science Foundation of Jiangsu Education Committee,China (Grant Nos. 09kjd110001 and 08kjb110011)Key Natural Science Foundation by the Bureau of Education of Anhui Province of China (Grant No. KJ2008A05ZC)Jiangsu Teachers University of Technology Foundation (Grant No. KYY08033)
文摘A class of oscillator of the EI Nifio-Southern oscillation model is considered. Using Mawhin＇s continuation theorem, a result on the existence of periodic solutions for ENSO model is obtained.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10271044)
文摘In this paper, the existence of two positive periodic solutions for a generalized delayed population model with an exploited term is established by using the continuation theorem of the coincidence degree theory.
基金supported by the National Natural Science Foundation of China under the Grant(10426010)the Foundation of Science and Technology of Fujian Province for Young Scholars(2004J0002)+3 种基金the Foundation of Fujian Education Bureau(JA04156)the National Natural Science Foundation of China under Grant 60373067the Natural Science Foundation of Jiangsu Province,China under Grants BK2003053Qing-Lan Engineering Project of Jiangsu Province,the Foundation of Southeast University,Nanjing,China under Grant XJ030714
文摘With the help of a continuation theorem based on Gaines and Mawhin＇s coincidence degree, several verifiable criteria are established for the global existence of positive periodic solutions of a class of non-autonomous single species population model with delays （both state-dependent delays and continuous delays） and feedback control. After that, by constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotic stable positive periodic solution of a kind of nonlinear feedback control ecosystem are obtained. Our results extend and improve the existing results, and have further applications in population dynamics.
基金National Natural Science Foundation of China (Grant No.10071022)Mathematical Tianyuan Foudation of China (Grant No.TY10026002-01-05-03) & Shanghai Priority Academic Research.
文摘By using the continuation theorem of Mawhin’s coincidence degree theory, a sufficient condition is derived for the existence of positive periodic solutions for a distributed delay competition model , where r <SUB>1</SUB> and r <SUB>2</SUB> are continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞) with are positive continuous ω-periodic functions in R <SUB>+</SUB> = [0,∞), b <SUB>i </SUB>(i = 1, 2) is nonnegative continuous ω-periodic function in R <SUB>+</SUB> = [0,∞), ω and T are positive constants, and . Some known results are improved and extended.
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.
基金Supported by the National Natural Science Foundation of China （No.19531070）
文摘In this paper, we study a non-autonomous ratio-dependent predator-prey model with exploited term. By means of the coincidence degree theory, we establish a sufficient condition for the existence of at least two positive periodic solutions of this model.
文摘By means of the theory of coincidence degree, sufficient condition for the existence of positive periodic solution to certain neutral delay competition model is obtained.
文摘In this paper, a three species diffusive predator-prey model with functional response is studied, where all parameters are time dependent. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for this system is established.
基金the Scientific Research Foundation of the Doctor Department of Hubei University of Technology
文摘In this paper, we study a non-autonomous ratio-dependent predator-prey model with predator＇s harvest. By means of the coincidence degree theory, we establish sufficient conditions for the existence of at least two positive periodic solutions of this model.
基金This work was supported by the Foundation of Developing Science and Technology of Fuzhou University under the grant 0030824594 and the Foundation of Fujian Education Bureau under the Grant JB03059.
文摘Discrete-time analogue of mutualism model is introduced. The discrete-time analogues is considered to be numerical discretization of the continuous-time models and we study their dynamical characteristics. It is shown that the discrete-time analogues preserve the periodicity of the continuous-time models.
基金This work was supported by the Foundation of Developing Science Technology of Fuzhou University under the grant 0030824594 the Foundation of Fujian Education Bureau under the Grant JB03059.
文摘In this paper, by using Mawhin coincidence degree, some sufficient conditions are obtained for the global existence of positive periodic solution of a mutualism system with infinite delays. Our results generalize those of Yang etc. [8] and Gopalsamy and He [7].
基金Supported by the National Natural Science Foundation of China (No.19971026,10271044).
文摘By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for a nonautonomous diffusive food chain system of three species.is established, where ri(t), aii(t) (i = 1.2,3,4), Di(t) (i = 1,2), a12(t), a21(t), a23(t) and a32(t) are all positive periodic continuous functions with period w > 0, Ti(i = 1,2) are positive constants.
基金The research is supported by the Scientific Research Foundation of the Doctor Department of Hubei University of Technology.
文摘The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.
基金Natural Science Foundation of Education Department of AnhuiProvince (KJ2008B236).
文摘In this paper, a predator-prey chain system with impulsive effects and Beddington-DeAngelis functional response is studied. We investigate the existence of periodic solu-tion by coincidence degree theory. Sufficient conditions are obtained for the existence of periodic solution.
