Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition

Wang, Zhen; Xie, Yingkang; Lu, Junwei; Li, Yuxia

doi:10.1016/j.amc.2018.11.016

Cited by 102 publications

(63 citation statements)

References 33 publications

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“…Therefore several researchers have investigated the stability of fractional order systems. Up to now, it has made great strides [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. The Lyapunov direct method (LDM) is one of the more important methods to analyze stability of fractional order systems.…”

Section: Introductionmentioning

confidence: 99%

Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System

et al. 2019

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Section: Introductionmentioning

confidence: 99%

Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System

et al. 2019

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“…Recently, Neimark-Sacker bifurcation related to discrete-time models has been investigated by many authors [19][20][21][22][23][24][25][26][27]. Furthermore, in the case of continuous systems, we refer to [28][29][30][31][32] for some recent discussions related to Hopf bifurcation. First, we show that the positive equilibrium (u * , ke -u * -1) of system (1.3) undergoes Hopf bifurcation such that k is selected as a bifurcation parameter.…”

Section: Neimark-sacker Bifurcationmentioning

confidence: 99%

Period-doubling and Neimark–Sacker bifurcations of plant–herbivore models

Elsayed

Din

2019

Adv Differ Equ

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The interaction between plants and herbivores plays a vital role for understanding community dynamics and ecosystem function given that they are the critical link between primary production and food webs. This paper deals with the qualitative nature of two discrete-time plant-herbivore models. In both discrete-time models, function for plant-limitation is of Ricker type, whereas the effect of herbivore on plant population and herbivore population growth rate are proportional to functional responses of type-II and type-III. Furthermore, we discuss the existence of equilibria and parametric conditions of topological classification for these equilibria. Our analysis shows that positive steady states of both discrete-time plant-herbivore models undergo flip and Hopf bifurcations. Moreover, we implement a hybrid control strategy, based on parameter perturbation and state feedback control, for controlling chaos and bifurcations. Finally, we provide some numerical simulations to illustrate theoretical discussion.

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“…Kuang et al investigated the relationship between the stability of the population and the dispersal rate of the prey species in [3]. When two species interact, one as a predator and the other as prey, then the Lotka-Volterra predator-prey model is frequently used to describe the dynamics of the biological system [8][9][10][11][12]. Cui [4] explored a nonautonomous dispersal predator-prey system and the sufficient conditions for persistence were obtained.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space

Liu

Chang

Meng

2019

Journal of Function Spaces

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In this paper, we investigate the stochastic dynamics of two dispersal predator-prey systems perturbed by white noise, impulsive effect, and regime switching. For the system just interrupted by white noise, we first prove that the stochastic impulsive system has a nontrivial positive periodic solution. Then the sufficient conditions for persistence in mean and extinction of the system are obtained. For the system with Markov regime switching, we verify it is ergodic and has a stationary distribution. And conditions for extinction of the prey species are established. Finally, we provide a series of numerical simulations to illustrate the theoretical analysis.

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Stability and bifurcation of a delayed generalized fractional-order prey–predator model with interspecific competition

Cited by 102 publications

References 33 publications

Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System

Generalized Mittag–Leffler Stability of Hilfer Fractional Order Nonlinear Dynamic System

Period-doubling and Neimark–Sacker bifurcations of plant–herbivore models

Asymptotic Analysis of Impulsive Dispersal Predator-Prey Systems with Markov Switching on Finite-State Space

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