Global attractivity of positive periodic solution for a Volterra model

Wang, Kai; Zhu, Yanling

doi:10.1016/j.amc.2008.04.005

Cited by 30 publications

(13 citation statements)

References 2 publications

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“…where a, b, c, d, r, δ, τ and σ are nonnegative almost periodic functions and m is a nonnegative constant. It is well known that Mawhin's continuation theorem of coincidence degree theory is an important method to investigate the existence of positive periodic solutions to some kinds of non-linear ecosystems (see [11][12][13][26][27][28][29][30][31][32][33][34]). However, it is difficult to use it to investigate the existence of positive almost periodic solutions of non-linear ecosystems.…”

Section: Example 1 Let Us Consider the Following Simple Population Mmentioning

confidence: 99%

Positive Almost Periodic Solutions for a Delayed Predator–Prey Model with Hassell-Varley Type Functional Response

Zhang

Pang

Liao

2016

MCA

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By means of a fixed point theorem of coincidence degree theory, sufficient conditions are established for the existence of a positive almost periodic solution to a kind of delayed predator-prey model with Hassell-Varley type functional response. The method used in this paper offers a possible means to study the existence of positive almost periodic solutions to the models in biological populations. Finally, an example as well as numerical simulations are given to illustrate the feasibility and effectiveness of our results.

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Section: Example 1 Let Us Consider the Following Simple Population Mmentioning

confidence: 99%

Positive Almost Periodic Solutions for a Delayed Predator–Prey Model with Hassell-Varley Type Functional Response

Zhang

Pang

Liao

2016

MCA

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“…Compared with the predator-prey system without mutual interference, the predator-prey system with mutual interference contains more dynamic behavior. For example, Wang and Zhu [28] proposed the existence of periodic solutions with mutual interference as follows:…”

Section: Introductionmentioning

confidence: 99%

On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

Wang

Liu

et al. 2020

Discrete Dynamics in Nature and Society

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In this paper, we present a predator-prey system with mutual interference and distributed time delay and study its dynamical behavior. Based on the existence and universality of mutual interference among species, it is necessary to further study an impulsive food web system. By using stability theory, slight perturbation technique, and comparison theorem, we obtain some theoretical results of the system, such as boundedness and permanence. Moreover, numerical experiments are used to verify the theoretical results and to explore the dynamical behavior of the system, which exhibits rich dynamical behavior such as chaotic oscillation, periodic oscillation, symmetry-breaking bifurcations, chaotic crises, and period bifurcation. Finally, we give some practical guidelines for biological systems based on the theoretical results and numerical experiments of the system.

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“…On the other hand, biological and environmental parameters cannot supposedly be constant throughout a time period as they are subject to fluctuate. Thus, the seasonal effects are considered as important selective forces on a system in a periodic environment . The strength of intraspecific competition also varies due to change in temperature, light intensity, and all other facts that are supposed to be changed with the season.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, the seasonal effects are considered as important selective forces on a system in a periodic environment. [36][37][38][39][40][41] The strength of intraspecific competition also varies due to change in temperature, light intensity, and all other facts that are supposed to be changed with the season. The effect of change of seasonal variation in the dynamics of the food web system in the presence of intraspecific competition in top predators is still an unexplored area.…”

Section: Introductionmentioning

confidence: 99%

Study on autonomous and nonautonomous version of a food chain model with intraspecific competition in top predator

Roy

Alam

2019

Math Methods in App Sciences

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In this article, a three‐species food chain model with intraspecific competition in top predators has been considered. Ecological and mathematical well posedness of the model system has been established by showing that all the solutions of the model are positive and bounded. The extinction scenarios of intermediate and top predator species along with the existence and stability of all equilibrium points have been discussed. The effects of competition and conversion efficiency of top predators in the dynamics of the system have been discussed with great thrust, and it is observed that the conversion efficiency of top predators deteriorates the stability of the system, whereas intraspecific competition in top predators enhances the stable coexistence of all the populations of the system. Further, nonautonomous version of the model system has been taken into consideration to study the impact of seasonal variation in the dynamics of the model system. Sufficient conditions for the existence of a globally attractive positive periodic have been established in a periodic environment. Finally, numerical simulations have been carried out to validate our analytical findings.

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Global attractivity of positive periodic solution for a Volterra model

Cited by 30 publications

References 2 publications

Positive Almost Periodic Solutions for a Delayed Predator–Prey Model with Hassell-Varley Type Functional Response

Positive Almost Periodic Solutions for a Delayed Predator–Prey Model with Hassell-Varley Type Functional Response

On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

Study on autonomous and nonautonomous version of a food chain model with intraspecific competition in top predator

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