An impulsive two-stage predator–prey model with stage-structure and square root functional responses

Ma, Xiangmin; Shao, Yuanfu; Wang, Zhen; Fang, Xianjia; Ju, Zhixiang

doi:10.1016/j.matcom.2015.08.009

Cited by 30 publications

(11 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For t > t, the same arguments can be followed since 1 for t > t * , the same arguments can be continued. Hence, x(t) ≥ m 1 for all t ≥ t.…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 98%

“…In the past few decades, food web or food chain predatorprey system has been widely studied by many scholars. Many researchers have obtained some classical theoretical knowledge of the predator-prey system and given some practical control strategies, regulation means, and simulation analysis; all these results can be found in these papers [1][2][3][4]. With the evolution and development of the ecological system, the relationships of dynamics between predators and prey will continue to be the significant theme of ecology and mathematics, since its existence and importance.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Wang

Liu

et al. 2020

Discrete Dynamics in Nature and Society

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…For t > t, the same arguments can be followed since 1 for t > t * , the same arguments can be continued. Hence, x(t) ≥ m 1 for all t ≥ t.…”

Section: Discrete Dynamics In Nature and Societymentioning

confidence: 98%

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…System (1) has been studied extensively in the past few years (see [16][17][18][19][20][21][22][23][24][25]). For example, in [16], by using fl as the bifurcation parameter, the authors showed that, as the parameter changes, the stability of the constant positive steady state varies, which induces the occurrence of Hopf bifurcating periodic solutions; however, their works tend to be numerical, rather than analytical.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator‐Prey System

Lin

Chai

Yang

et al. 2019

Mathematical Problems in Engineering

View full text Add to dashboard Cite

In this paper, we consider a diffusive predator-prey system where the prey exhibits the herd behavior in terms of the square root of the prey population. The model is supposed to impose on homogeneous Neumann boundary conditions in the bounded spatial domain. By using the abstract Hopf bifurcation theory in infinite dimensional dynamical system, we are capable of proving the existence of both spatial homogeneous and nonhomogeneous periodic solutions driven by Hopf bifurcations bifurcating from the positive constant steady state solutions. Our results allow for the clearer understanding of the mechanism of the spatiotemporal pattern formations of the predator-prey interactions in ecology.

show abstract

“…Похожие работы, направленные на изучение возникающих динамических режимов, проводятся и на основе аппарата дифференциальных уравнений, например [29,30]. Нередко встречаются исследования, посвященные изучению динамики сообществ типа «хищник -жертва», когда жертва или хищник представлены несколькими видами [8,[31][32][33][34][35][36][37], или же когда одна из составляющих сообщества подвергается изъятию [38][39][40].В работах, посвященных изучению динамики системы «хищник -жертва» с учетом возрастной детализации или стадий развития, используются в основном модели с непрерывным временем [41][42][43][44][45][46][47][48][49][50][51][52][53], при этом системы с дискретным временем применяются реже [54][55][56]. В частности, можно выделить работы, в которых рассматривается влияние возрастной структуры либо хищника [42,55], либо жертвы на развитие сообщества [56][57][58].…”

unclassified

“…В работах, посвященных изучению динамики системы «хищник -жертва» с учетом возрастной детализации или стадий развития, используются в основном модели с непрерывным временем [41][42][43][44][45][46][47][48][49][50][51][52][53], при этом системы с дискретным временем применяются реже [54][55][56]. В частности, можно выделить работы, в которых рассматривается влияние возрастной структуры либо хищника [42,55], либо жертвы на развитие сообщества [56][57][58].…”

unclassified

Modeling the Dynamics of Predator-Prey Community with Age Structures

Неверова¹,

Zhdanova²,

Frisman³

2019

Math.Biol.Bioinf.

View full text Add to dashboard Cite

A model of the predator-prey community has been proposed with specific stages of individual development and the seasonality of breeding processes. It is assumed each of the species has an age structure with two stages of development. The case typical for the community “Arctic fox – rodents” is modeled. An analytical and numerical study of the model proposed is made. It is shown that periodic, quasi-periodic and chaotic oscillations can occur in the system, as well as a shift in the dynamics mode as a result of changes in the current sizes of the community’s populations. The model proposed demonstrates long-period oscillations with time delay like auto-oscillations in the classical model of Lotka-Volterra. It is shown that a transition from stable dynamics to quasi-periodic oscillations and vise verse is possible in the system, while an increase in the values of the half capturing saturation coefficient reduces the possibility of quasiperiodic oscillation emergence. Simulations demonstrate the growth in predator’s consumption of the prey average number expands the zones of multistability and quasi-periodic dynamics in the stability area of nontrivial fixed point. Therefore, the variation of the current population size of the community can lead to a change in the dynamic mode observed. The scenarios of transition from stationary dynamics to community’s population fluctuations are analyzed with different values of population parameters determining the dynamics of both species and their interaction coefficient. The model shows both sustainable community development and various complex fluctuations of interacting species. At the same time, the prey dynamics affects the predator one: the prey population fluctuations initiate predator oscillations like prey’s fluctuations, while the intrapopulation parameters of the predator can give to both stationary and fluctuating dynamic modes.

show abstract

An impulsive two-stage predator–prey model with stage-structure and square root functional responses

Cited by 30 publications

References 28 publications

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

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

Spatiotemporal Patterns Induced by Hopf Bifurcations in a Homogeneous Diffusive Predator‐Prey System

Modeling the Dynamics of Predator-Prey Community with Age Structures

Contact Info

Product

Resources

About