Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays

Yuan, Jialei; Zhao, Lingzhi; Huang, Chengdai; Xiao, Min

doi:10.1016/j.matcom.2020.10.013

Cited by 26 publications

(11 citation statements)

References 25 publications

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“…Considering a population of the walkers performing a Lévy-flight mobility pattern leads to a fractional-order reaction-diffusion equation whose solution represents the walker densities [18,27]. From an applied point of view, fractional-order models have been used in a broad range of problems in ecology [28,29], biology [30], plasma turbulence [31,32], finance [33] and also recently numerous studies have been conducted on the subjects of bifurcation analysis, stability, and optimal control of fractional-order systems, such as predator-prey models [34,35], diffusive mussel-algae models [36], and neural networks [37][38][39]. As an application of space fractional-order diffusion equations in epidemiology, Hanert et al [40] have shown that such equations can be applied to model the modern epidemics, such as avian influenza, and even SARS and also that the fractionalorder diffusion operators make the epidemic waves travel at an exponential speed and the tails of the wave solutions decay algebraically as a power-law.…”

Section: Introductionmentioning

confidence: 99%

Front Propagation of Exponentially Truncated Fractional-Order Epidemics

Farhadi

Hanert

2022

Fractal Fract

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The existence of landscape constraints in the home range of living organisms that adopt Lévy-flight movement patterns, prevents them from making arbitrarily large displacements. Their random movements indeed occur in a finite space with an upper bound. In order to make realistic models, by introducing exponentially truncated Lévy flights, such an upper bound can thus be taken into account in the reaction-diffusion models. In this work, we have investigated the influence of the λ-truncated fractional-order diffusion operator on the spatial propagation of the epidemics caused by infectious diseases, where λ is the truncation parameter. Analytical and numerical simulations show that depending on the value of λ, different asymptotic behaviours of the travelling-wave solutions can be identified. For small values of λ (λ≳0), the tails of the infective waves can decay algebraically leading to an exponential growth of the epidemic speed. In that case, the truncation has no impact on the superdiffusive epidemics. By increasing the value of λ, the algebraic decaying tails can be tamed leading to either an upper bound on the epidemic speed representing the maximum speed value or the generation of the infective waves of a constant shape propagating at a minimum constant speed as observed in the classical models (second-order diffusion epidemic models). Our findings suggest that the truncated fractional-order diffusion equations have the potential to model the epidemics of animals performing Lévy flights, as the animal diseases can spread more smoothly than the exponential acceleration of the human disease epidemics.

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Section: Introductionmentioning

confidence: 99%

Front Propagation of Exponentially Truncated Fractional-Order Epidemics

Farhadi

Hanert

2022

Fractal Fract

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“…For example, Kaslik and Rȃdulescu [33] discussed the Hopf bifurcation of fractional-order gene regulatory networks. Yuan et al [34] dealt with the bifurcation behavior of a fractionalorder delayed prey-predator system. Xue et al [35] applied command-filtering and a sliding mode technique to investigate the adaptive fuzzy finite-time backstepping control of a fractional nonlinear model.…”

Section: Introductionmentioning

confidence: 99%

Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Gao

et al. 2022

Fractal Fract

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In this current manuscript, we study a fractional-order modificatory hybrid optical model (FOMHO model). Experiments manifest that under appropriate parameter conditions, the fractional-order modificatory hybrid optical model will generate chaotic behavior. In order to eliminate the chaotic phenomenon of the (FOMHO model), we devise two different control techniques. First of all, a suitable delayed feedback controller is designed to control chaos in the (FOMHO model). A sufficient condition ensuring the stability and the occurrence of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is set up. Next, a suitable delayed mixed controller which includes state feedback and parameter perturbation is designed to suppress chaos in the (FOMHO model). A sufficient criterion guaranteeing the stability and the onset of Hopf bifurcation of the fractional-order controlled modificatory hybrid optical model is derived. In the end, software simulations are implemented to verify the accuracy of the devised controllers. The acquired results of this manuscript are completely new and have extremely vital significance in suppressing chaos in physics. Furthermore, the exploration idea can also be utilized to control chaos in many other differential chaotic dynamical models.

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“…For example, Xu et al [14] reported the Hopf bifurcation of fractional-order BAM neural networks including multiple time delays; Yuan et al [15] studied the stability and Hopf bifurcation for a fractional-order prey-predator system including two different time delays;…”

Section: Introductionmentioning

confidence: 99%

Bifurcation dynamics in a fractional-order oregonator model including time delay

Xu¹,

Economics²,

Zhang³

et al. 2021

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Setting up mathematical models to describe the interaction of chemical variables has been a hot issue in chemical and mathematical areas. Nevertheless, many mathematical models are only involved with the integer-order differential equation case. The fruits on fractional-order chemical models are very scarce. In this present work, on the basis of the previous studies, we set up a novel fractional-order delayed Oregonator model. Selecting the time delay as bifurcation parameter, we obtain novel delay-independent bifurcation conditions that guarantee the stability and the appearance of Hopf bifurcation for the fractional-order delayed Oregonator model. The study shows that time delay plays a vital role in controlling the stability and the appearance of Hopf bifurcation of the considered fractional-order delayed Oregonator model. In order to verify the rationality of theoretical results, computer simulations are carried out.

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Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays

Cited by 26 publications

References 25 publications

Front Propagation of Exponentially Truncated Fractional-Order Epidemics

Front Propagation of Exponentially Truncated Fractional-Order Epidemics

Chaos Suppression of a Fractional-Order Modificatory Hybrid Optical Model via Two Different Control Techniques

Bifurcation dynamics in a fractional-order oregonator model including time delay

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