In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only...In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only obtain necessary as well as sufficient and necessary conditions for the oscillation of ail eventually positive solutions about the positive equilibrium, but also obtain some sufficient conditions for the convergence of eventually positive solutions. Furthermore, authors also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded.展开更多
The discrete dynamics for competition populations of Lotka-Volterra type modeled as N1(t+1)=N1(t) exp[r1(1-N1-b12N2)], N2(t+1)=N2(t) exp[r2(1-N2-b21N1)] is considered in the paper. In the case of non-persistence the a...The discrete dynamics for competition populations of Lotka-Volterra type modeled as N1(t+1)=N1(t) exp[r1(1-N1-b12N2)], N2(t+1)=N2(t) exp[r2(1-N2-b21N1)] is considered in the paper. In the case of non-persistence the attractive behavior of model has been discussed. Especially, there are two attractive sets when h_(ij)>1, and the attractive behaviors are more complicated than that of the corresponding cofitinuous model. The attracted regions are given. We prove that the model is also persistent in the degenerate case of b_(ij)=1. In the persistence case of b_(ij)<1, the existence and uniqueness for two-period points of the model are studied at r1=r2. The condition for the multi-pair of two-period points is indicated and their influences on population dynamical behaviors are shown.展开更多
Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive soluti...Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive solution and the property of stochastically ultimate boundedness of model(1.1)are proved.Moreover,the extinction and the persistence of the disease are established.The results are verified by numerical simulations.展开更多
This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov...This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.展开更多
We propose and study a predator prey model with state-dependent delay where the prey population is assumed to have an age structure. The state-dependent delay appears due to the mature condition that the prey must spe...We propose and study a predator prey model with state-dependent delay where the prey population is assumed to have an age structure. The state-dependent delay appears due to the mature condition that the prey must spend an amount of time in the immature stage sufficient to accumulate a threshold amount of food. We perform a qualitative analysis of the solutions, which includes studying positivity and boundedness, existence and local stability of equilibria. For the global dynamics of the system, we discuss an attracting region which is determined by solutions, and the region collapses to the interior equilibrium in the constant delay case.展开更多
This paper is concerned with a three-species competitive model with both white noises and Levy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between ...This paper is concerned with a three-species competitive model with both white noises and Levy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between persistence in the mean and extinction for each species. The sufficient criteria for stability in distribution of solutions are obtained. Finally, numerical simulations are carried out to verify the theoretical results.展开更多
A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochasti...A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.展开更多
文摘In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only obtain necessary as well as sufficient and necessary conditions for the oscillation of ail eventually positive solutions about the positive equilibrium, but also obtain some sufficient conditions for the convergence of eventually positive solutions. Furthermore, authors also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded.
文摘The discrete dynamics for competition populations of Lotka-Volterra type modeled as N1(t+1)=N1(t) exp[r1(1-N1-b12N2)], N2(t+1)=N2(t) exp[r2(1-N2-b21N1)] is considered in the paper. In the case of non-persistence the attractive behavior of model has been discussed. Especially, there are two attractive sets when h_(ij)>1, and the attractive behaviors are more complicated than that of the corresponding cofitinuous model. The attracted regions are given. We prove that the model is also persistent in the degenerate case of b_(ij)=1. In the persistence case of b_(ij)<1, the existence and uniqueness for two-period points of the model are studied at r1=r2. The condition for the multi-pair of two-period points is indicated and their influences on population dynamical behaviors are shown.
基金This work is supported by the National Natural Science Foundation of China(No.11701495)Scientific and Technological Key Projects of Henan Province(No.192102310193)Nanhu Scholars Program for Young Scholars of XYNU.
文摘Dynamical behaviors of a siocluustic periodic SIRS epidemic model with time delay are investigated.By constructing suitable Lyapunov functions and applying Ito's formula,the existence of the global positive solution and the property of stochastically ultimate boundedness of model(1.1)are proved.Moreover,the extinction and the persistence of the disease are established.The results are verified by numerical simulations.
基金supported by the National Natural Science Foundation of China(Nos.11901398,11671149,11871225 and 11771102)Guangdong Basic and Applied Basic Research Foundation(No.2019A1515011350)the Fundamental Research Funds for the Central Universities(No.2018MS58).
文摘This paper investigates a stochastic Holling II predator-prey model with Levy jumps and habit complexity.It is first proved that the established model admits a unique global positive solution by employing the Lyapunov technique,and the stochastic ultimate boundedness of this positive solution is also obtained.Sufficient conditions are established for the extinction and persistence of this solution.Moreover,some numerical simulations are carried out to support the obtained results.
文摘We propose and study a predator prey model with state-dependent delay where the prey population is assumed to have an age structure. The state-dependent delay appears due to the mature condition that the prey must spend an amount of time in the immature stage sufficient to accumulate a threshold amount of food. We perform a qualitative analysis of the solutions, which includes studying positivity and boundedness, existence and local stability of equilibria. For the global dynamics of the system, we discuss an attracting region which is determined by solutions, and the region collapses to the interior equilibrium in the constant delay case.
基金The work is supported by National Science Foundation of China （No. 11472298）, the Fundamental Research Funds for the Central Universities （No. ZXH2012K004）, the National Science Foundation of Tianjin City （No. 13JCQNJC04400） and the NNSF of P. R. China （No. 11401574）.
文摘This paper is concerned with a three-species competitive model with both white noises and Levy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between persistence in the mean and extinction for each species. The sufficient criteria for stability in distribution of solutions are obtained. Finally, numerical simulations are carried out to verify the theoretical results.
基金This work was supported by the National Natural Science Foundation of P. R. China （No. 11171081, 11171056）, the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology （No. HIT.NSRIF.2011094）, and the Scientific Research Foundation of Harbin Institute of Technology at Weihai （No. HIT （WH） ZB201103）.
文摘A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.
