Multiple periodic solutions for impulsive Gause-type ratio-dependent predator-prey systems with non-monotonic numerical responses

This paper investigates the existence of multiple periodic solutions for impulsive Gause-type ratio-dependent predator-prey systems with non-monotonic numerical responses and time delays. Some sufficient conditions are derived by using the continuation theorem of coincidence degree theory and analysis technique. As corollaries, some applications are listed. In particular, the presented criteria improve and extend many previous results in the literature.     

Existence of positive periodic solutions for an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays

In this paper, we propose an impulsive semi-ratio-dependent predator-prey model with dispersion and time delays. By applying the continuation theorem of coincidence degree theory, we establish a set of sufficient conditions on the existence of at least one positive periodic solution. The result not only improves but also generalizes that for the case without pulses.     

Positive periodic solutions for impulsive Gause-type predator-prey systems

This paper is devoted to impulsive periodic Gause-type predator-prey systems with monotonic or non-monotonic numerical responses. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones.     

Positive periodic solutions in delayed Gause-type predator-prey systems

By using a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions in delayed Gause-type predator-prey systems. Some known results are shown to be special cases of the presented paper.     

具有时滞的半比率依赖型捕食者-食饵系统的周期性

A delayed semi-ratio-dependent predator-prey system in a periodic environment is investigated in this paper. By using a continuation theorem based on Gaines and Mawhin‘s coincidence degree,the global existence of positive periodic solution is studied. A set of easily verifiable sufficient conditions are obtained.     

Dynamics of a class of nonautonomous semi-ratio-dependent predator-prey systems with functional responses

In this paper, we investigate the dynamics of a class of the so-called semi-ratio-dependent predator-prey interaction models with functional responses based on systems of nonautonomous differential equations with time-dependent parameters. The functional responses are classified into five types and typical examples of each type are provided. Then we establish sufficient criteria for the boundedness of solutions, the permanence of system, and the existence, uniqueness and globally asymptotic stability of positive periodic solution and positive almost periodic solution. Some conclusive discussion is presented at the end of this paper.     

A note on periodic solutions of nonautonomous second-order systems

A multiplicity theorem is obtained for periodic solutions of nonautonomous second-order systems with partially periodic potentials by the minimax methods.

     

Periodic solutions of a periodic delay predator-prey system

The existence of a positive periodic solution for

is established, where , , , , are positive periodic continuous functions with period , and , are periodic continuous functions with period .

     

Uniform persistence of the periodic predator-prey lotka-volterra systems

In this paper we give the sufficient and necessary conditions of the uniform persistence for periodic predator-prey Lotka- Volterra systems. That is, the system is uniformly persistent if and only if any one of the semi-trivial periodic solutions is linearly unstable.     

Multiple periodic solutions for second order systems with changing sign potential

This paper deals with the multiplicity of solutions of a second order nonautonomous system. We extend a previous result of the author relaxing the assumptions on the sign of the potential.     

Holling IV捕食-食饵时滞系统的多个周期解

应用重合度定理研究了一类具有Holling IV类功能性反应时滞捕食-食饵系统的周期解的存在性问题,建立了该系统具有至少两个正周期解的充分条件．     

Existence of periodic solutions in predator-prey with Watt-type functional response and impulsive effects

In this paper, the existence of a periodic solution and the permanence of a periodic Watt-type predator-prey system where the prey disperses in patchy environment with two patches are investigated. With the continuation theorem of coincidence degree theory, we obtain the existence of a positive periodic solution for such a system. We assume the Watt-type functional response within-patch dynamics and provide a sufficient condition to guarantee the predator and prey species to be permanent. Furthermore, we give numerical analysis to confirm our theoretical results. It will be useful to ecosystem control.     

具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

Computation of periodic solutions of Hamiltonian systems

This paper attempts to give a practical method to compute global periodic solutions of autonomous Hamiltonian systems of arbitrary finite order. The proposed numerical method is based on continuation of solutions branching from equlibrium points and requires no iterations. Moreover, during computation of one-parameter families of periodic orbits, their possible bifurcations are determined as well.     

Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system

We consider a delayed predator-prey system. We first consider the existence of local Hopf bifurcations, and then derive explicit formulas which enable us to determine the stability and the direction of periodic solutions bifurcating from Hopf bifurcations, using the normal form theory and center manifold argument. Special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu [Trans. Amer. Math. Soc. 350 (1998) 4799], we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are also given.     

Existence of periodic and subharmonic solutions for second order functional difference equations

In this paper, by using the critical point theory, the existence of periodic and subharmonic solutions to a class of second order functional difference equations is obtained. The main approach used in our paper is variational technique and the Saddle Point Theorem. The problem is to solve the existence of periodic and subharmonic solutions of second order forward and backward difference equations.     

Existence of periodic solutions of sublinear Hamiltonian systems

The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need additional conditions to ensure the existence of periodic bouncing solutions.     

Uniform persistence and periodic solutions for a discrete predator-prey system with delays

In this paper, we deal with a discrete predator-prey system with delay. We first give a sufficient condition for the uniform persistence of the system. Assuming that the coefficients in the system are periodic, by generalizing the Yoshizawa's theorem on the existence of periodic solution for ordinary differential equations to the difference equations with delays, we obtain the existence of a periodic solution basing on the uniform persistence result.