共查询到20条相似文献,搜索用时 578 毫秒
1.
《Chaos, solitons, and fractals》2006,27(4):980-990
The effect of periodic forcing and impulsive perturbations on predator–prey model with Holling type IV functional response is investigated. The periodic forcing is affected by assuming a periodic variation in the intrinsic growth rate of the prey. The impulsive perturbations are affected by introducing periodic constant impulsive immigration of predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can easily give rise to complex dynamics, including (1) quasi-periodic oscillating, (2) period doubling cascade, (3) chaos, (4) period halfing cascade. 相似文献
2.
《Chaos, solitons, and fractals》2005,23(2):631-643
Predator–prey system with non-monotonic functional response and impulsive perturbations on the predator is established. By using Floquet theorem and small amplitude perturbation skills, a locally asymptotically stable prey-eradication periodic solution is obtained when the impulsive period is less than the critical value. Otherwise, if the impulsive period is larger than the critical value, the system is permanent. Further, using numerical simulation method the influences of the impulsive perturbations on the inherent oscillation are investigated. With the increasing of the impulsive value, the system displays a series of complex phenomena, which include (1) quasi-periodic oscillating, (2) period-doubling, (3) period-halfing, (4) non-unique dynamics (meaning that several attractors coexist), (5) attractor crisis and (6) chaotic bands with periodic windows. 相似文献
3.
研究捕食者具有非单调功能反应和周期脉冲扰动的捕食者一食饵系统,利用脉冲微分方程的Floquet理论和比较定理,得到了系统灭绝和持续生存的充分条件.最后,通过数值模拟阐明系统在周期脉冲扰动下的复杂性. 相似文献
4.
A periodic single-species model with periodic impulsive perturbations was investigated. By using Brouwer’s fixed point theorem and the Lyapunov function, sufficient conditions for the existence and global asymptotic stability of positive periodic solutions of the system were derived. Numerical simulations were presented to verify the feasibilities of our main results. 相似文献
5.
Gani T. Stamov 《Journal of Applied Mathematics and Computing》2008,27(1-2):243-255
By means of piecewise continuous functions Lyapunov’s functions we give new sufficient conditions for the global exponential stability of the unique positive almost periodic solutions of an non autonomous N-dimensional impulsive Lotka-Volterra diffusive competitive system with dispersion and fixed moments of impulsive perturbations. 相似文献
6.
7.
具有非单调功能反应和脉冲扰动的捕食系统的分析 总被引:2,自引:1,他引:1
研究捕食者具有非单调功能反应和周期脉冲扰动的食饵-捕食系统,利用脉冲微分方程的F loquet理论和比较定理,得到了系统灭绝和持续生存的充分条件. 相似文献
8.
In this paper, on the basis of the theories and methods of ecology and ordinary differential equation, a food web system with impulsive perturbations and distributed time delay is established. By using the theories of impulsive equation, small amplitude perturbation skills and comparison technique, we get the condition which guarantees the global asymptotical stability of the prey and intermediate predator eradication periodic solution. On this basis, we get that the food web system is permanent if some parameters are satisfied with certain conditions. In order to show that these conditions are effective, the influences of impulsive perturbations on the inherent oscillation and distributed time delay are studied numerically; these show rich dynamics, such as period-halving bifurcation, chaotic band, narrow or wide periodic window, chaotic crises. Moreover, the computation of the largest Lyapunov exponent shows the chaotic dynamic behavior of the model. Meanwhile, we investigate the qualitative nature of strange attractor by using Fourier spectra. All of these results may be useful in the study of the dynamic complexity of ecosystems. 相似文献
9.
The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy 总被引:5,自引:0,他引:5
In this paper, by using theories and methods of ecology and ordinary differential equation, the dynamics complexity of a prey–predator system with Beddington-type functional response and impulsive control strategy is established. Conditions for the system to be extinct are given by using the Floquet theory of impulsive equation and small amplitude perturbation skills. Furthermore, by using the method of numerical simulation with the international software Maple, the influence of the impulsive perturbations on the inherent oscillation is investigated, which shows rich dynamics, such as quasi-periodic oscillation, narrow periodic window, wide periodic window, chaotic bands, period doubling bifurcation, symmetry-breaking pitchfork bifurcation, period-halving bifurcation and crises, etc. The numerical results indicate that computer simulation is a useful method for studying the complex dynamic systems. 相似文献
10.
In this paper, we investigate a three trophic level food chain system with Holling II functional responses and periodic constant impulsive perturbations of top predator. Conditions for extinction of predator as a pest are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of predator eradication periodic solution. Further, influences of the impulsive perturbation on the inherent oscillation are studied numerically, which shows the rich dynamics (for example: period doubling, period halfing, chaos crisis) in the positive octant. The dynamics behavior is found to be very sensitive to the parameter values and initial value. 相似文献
11.
In this paper, a biochemical model with the impulsive perturbations is considered. By using the Floquet theorem, we find the boundary-periodic solution is asymptotically stable if the impulsive period is larger than a critical value. On the contrary, it is unstable if the impulsive period is less than the critical value. The problem of finding nontrivial periodic solutions is reduced to showing the existence of the nontrivial fixed points for the associated stroboscopic mapping of time snapshot equal to the common period of input. It is then shown that once a threshold condition is reached, a stable nontrivial periodic solution emerges via a supercritical bifurcation. Furthermore, influences of the impulsive input on the inherent oscillations are studied numerically, which shows the rich dynamics in the positive octant. 相似文献
12.
本文考虑一类具有脉冲扰动的比率相关的捕食者一食饵扩散模型,利用比较原理研究了这类系统的持续生存和灭绝性,通过将脉冲反应扩散方程转化为相应的算子方程,并证明了解在适当空间的紧性,得到了周期解的存在性、唯一性和全局稳定性.最后分析了脉冲效应对系统性态的影响. 相似文献
13.
Qi Wang Hongyan Zhang Minmin Ding Zhijie Wang 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3688-3697
In this paper, we study the existence of almost periodic solutions of a delay logistic model with fixed moments of impulsive perturbations. By using a comparison theorem and constructing a suitable Lyapunov functional, a set of sufficient conditions for the existence and global attractivity of a unique positive almost periodic solution is obtained. As applications, some special models are studied; our new results improve and generalize former results. 相似文献
14.
A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics. 相似文献
15.
《Chaos, solitons, and fractals》2006,27(3):768-777
In this paper, the dynamic complexities of a three trophic level food chain system with impulsive perturbations and Beddington–DeAngelis functional responses is studied. Conditions for extinction of predator are given. By using the Floquet theory of impulsive equation and small amplitude perturbation skills, we consider the local stability of predator eradication periodic solution. Further, influences of the impulsive perturbation on the inherent oscillation are studied numerically, which shows the rich dynamics in the positive octant. 相似文献
16.
Global dynamics of the periodic logistic system with periodic impulsive perturbations 总被引:1,自引:0,他引:1
This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions. 相似文献
17.
Zhao Yuxiao Wang Linshan Wang Yangfan 《Methodology and Computing in Applied Probability》2021,23(3):859-872
Methodology and Computing in Applied Probability - In this paper, the periodic solutions of a stochastic two-prey one-predator model with impulsive perturbations in a polluted environment are... 相似文献
18.
《Communications in Nonlinear Science & Numerical Simulation》2011,16(4):2041-2053
We study a predator–prey system with a Michaelis–Menten functional response and impulsive perturbations which contain chemical and biological control terms. By applying the Floquet theory, we establish conditions for the existence and stability of prey-free solutions of the system. We also show the existence of a positive periodic solution of the system by using the bifurcation theorem and find a sufficient condition that makes the system permanent. Moreover, numerical results on impulsive perturbations show that the system we consider can give birth to various kinds of dynamical behaviors. 相似文献
19.
A kind of predator-prey system of Holling type Ⅱ and interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory. 相似文献
20.
A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory. 相似文献