Stability, bifurcation and chaos control of a discretized Leslie prey-predator model

Akhtar, Shahnaz; Ahmed, Rizwan; Batool, Mehvish; Shah, Nehad Ali; Chung, Jae Dong

doi:10.1016/j.chaos.2021.111345

Cited by 22 publications

(8 citation statements)

References 11 publications

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“…Notably, a growing number of researchers have adopted the framework of bounded rationality to investigate economic models, as exemplifed by studies conducted by [13,14]. Te authors of [15] have analyzed the dynamic behavior of discretizing a continuous-time Leslie prey-predator model. Te authors of [16] have examined complex behavior in investment patterns within spatial public goods games.…”

Section: Literature Reviewmentioning

confidence: 99%

The Complexities in the R&D Competition Model with Spillover Effects in the Supply Chain

Xiao,

Xiao

2024

Complexity

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This study aims to investigate the research and development (R&D) competition within the supply chain, focusing on two aspects: R&D competition at the manufacturing level and competition in pricing strategies. This paper establishes a dynamic game model of R&D competition, comprising two manufacturers and two retailers, with both manufacturers exhibiting bounded rationality. The key findings are as follows: (1) an increase in the adjustment speed positively affects the chaotic nature of the R&D competition system, leading to a state of disorder. This chaotic state has adverse implications for manufacturing profitability. (2) The spillover effect exhibits a positive relationship with the level of chaos in the R&D competition system. A greater spillover effect contributes to a more turbulent environment, which subsequently impacts the profitability of manufacturers. (3) R&D cost parameters exert a positive influence on the stability of the R&D competition system. When the system reaches a state of equilibrium, an escalation in the R&D cost parameters poses a threat to manufacturer profitability. (4) Retailer costs play a detrimental role in the stability of the R&D competition system. As retailer costs increase, there is a decline in R&D levels, thereby diminishing manufacturer profitability. (5) To mitigate the chaotic state, we propose the implementation of the time-delayed feedback control (TDFC) method, which reflects a more stable state in the R&D competition system.

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Section: Literature Reviewmentioning

confidence: 99%

The Complexities in the R&D Competition Model with Spillover Effects in the Supply Chain

Xiao,

Xiao

2024

Complexity

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“…Improper management of bifurcations can lead to disturbances in population dynamics and the consequent destruction of ecosystems. For a detailed bifurcation analysis, we recommend that readers refer to [31,[33][34][35][36][37][38][39].…”

Section: Local Bifurcation Analysismentioning

confidence: 99%

Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior

Ahmed,

Almatrafi

2023

Int. J. Anal. Appl.

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The complex dynamics of a predator-prey system in discrete time are studied. In this system, we consider the prey’s Gompertz growth and the square-root functional response. The existence of fixed points and stability are examined. Using the center manifold and bifurcation theory, we found that the system undergoes transcritical bifurcation, period-doubling bifurcation, and Neimark-Sacker bifurcation. In addition, numerical examples are presented to illustrate the consistency of the analytical findings. The bifurcation diagrams show that the positive fixed point is stable if the death rate of the predator is greater than a threshold value. Biologically, it means that to prevent the predator population from growing uncontrollably and stability of the positive fixed point, the predator’s death rate should be greater than the threshold value.

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“…Chaos widely exists in many areas, such as astronomy, quantum mechanics, economy and finance, weather, climate, network science, thermodynamics, chemistry, probabilistic mathematics, fluid mechanics and so on [1][2][3][4][5][6][7]. The study indicates that chaos has a very important application value in power system protection, flow dynamics, biomedicine, computer technique, information science, cryptology, communication engineering and so on [8].…”

Section: Introductionmentioning

confidence: 97%

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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Stability, bifurcation and chaos control of a discretized Leslie prey-predator model

Cited by 22 publications

References 11 publications

The Complexities in the R&D Competition Model with Spillover Effects in the Supply Chain

The Complexities in the R&D Competition Model with Spillover Effects in the Supply Chain

Complex Dynamics of a Predator-Prey System With Gompertz Growth and Herd Behavior

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

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