Bifurcation analysis and chaos control in discrete-time eco–epidemiological models of pelicans at risk in the Salton Sea

Din, Qamar; Ishaque, Waqas

doi:10.1007/s40435-019-00508-x

Cited by 11 publications

(8 citation statements)

References 42 publications

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“…Romeiras et al (1992) developed a pole-placement method, also known as the generalized OGY method (Ogata, 2010). Furthermore, many scholars proposed state-feedback designs for controlling chaos in discrete-time systems, we refer to He et al (2014), Ghandchi-Tehrani et al (2015), Mobayen et al (2017), Din (2018a), Din et al (2018), Din (2018c), Din (2017a) and Din and Ishaque (2020), and the references therein.…”

Section: Chaos Controlmentioning

confidence: 99%

“…Also, we have investigated the stability at positive fixed point, bifurcation analysis, and chaos control. A lot of work done by many researchers have been cited by Peng et al (2017), Chen et al (2013), Cheng and Cao (2016), Ishaque et al (2019), Din (2019), Ma et al (2020), and Din and Ishaque (2020). To do so, we use the discrete-time form in case of non-overlapping generations with comprehensive theoretical discussions.…”

Section: Introductionmentioning

confidence: 99%

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Mutual interference and its effects on searching efficiency between predator–prey interaction with bifurcation analysis and chaos control

Ishaque

Din²,

Taj

2021

Journal of Vibration and Control

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In this paper, we study the dynamic of the predator–prey model based on mutual interference and its effects on searching efficiency. The parametric conditions, existence, and stability for trivial and boundary equilibrium points are studied. Also, it has shown that by applying the center manifold theorem and bifurcation theory, system undergoes Neimark–Sacker bifurcation across the neighborhood of a positive fixed point. Moreover, due to the bifurcation and chaos which objectively exist in a system, three chaos control strategies are designed and used. Moreover, to validate our theoretical and analytical discussions, numerical simulations are applied to show complex and chaotic behavior. Finally, theoretical discussions are validated with experimental field data.

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Section: Chaos Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mutual interference and its effects on searching efficiency between predator–prey interaction with bifurcation analysis and chaos control

Ishaque

Din²,

Taj

2021

Journal of Vibration and Control

Self Cite

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“…A limited number of contributions have recently been made to the study of the dynamics of 3-D discrete systems (Khan and Javaid 2021;Abdelaziz et al 2020;Din and Ishaque 2019;Feng et al 2021;Hu et al 2014;Ishaque et al 2019;Qin et al 2016;Xin et al 2010). For example, a discrete-time SIR epidemic models discussed in (Abdelaziz et al 2020;Hu et al 2014), in (Xin et al 2010) the authors investigated discrete financial system and in (Qin et al 2016), the authors studied discrete chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and 0-1 Chaos Test of a Discrete T System

Rana

2023

Chaos Theory and Applications

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This study examines discrete-time T system. We begin by listing the topological divisions of the system's fixed points. Then, we analytically demonstrate that a discrete T system sits at the foundation of a Neimark Sacker(NS) bifurcation under specific parametric circumstances. With the use of the explicit Flip-NS bifurcation criterion, we establish the flip-NS bifurcation's reality. Center manifold theory is then used to establish the direction of both bifurcations. We do numerical simulations to validate our theoretical findings. Additionally, we employ the $0-1$ test for chaos to demonstrate whether or not chaos exists in the system. In order to stop the system's chaotic trajectory, we ultimately employ a hybrid control method.

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“…Recently, a very short number of contributions dedicated to study the dynamics of three dimensional discrete systems [1,5,8,9,11,13,19,27]. For example, discrete-time epidemic models SIR, SEIR and hypertensive or diabetic exposed to COVID-19 discussed in [1,9,13] respectively, in [27] the authors investigated discrete financial system and in [19], the authors studied discrete chaotic system.…”

Section: Introductionmentioning

confidence: 99%

“…Neimark-Sacker bifurcation for discrete-time food chain model studied in [8]. The studies in [5,11] investigated discrete population models.These studies used only explicit (Flip-NS bifurcaton) criterion and numerical simulations for existence of flip and NS bifurcations. Chaos is strongly hooked into the initial conditions for the answer trajectories, or the exponential aberration in solution trajectories for little differences within the initial conditions in discrete system.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Discrete-Time Chaotic Lü System

Rana

Uddin

2022

Pan-Amer. J. Math.

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A discrete-time chaotic Lü system is investigated. Firstly, we give the conditions of local stability of this system around feasible fixed points. Then, we show analytically that discretized Lü system undergoes a flip-Neimark Sacker (NS) bifurcation when one of the system parameter varies near its critical value. We confirm the existence of flip-NS bifurcation via explicit Flip-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory and bifurcation theory. We carry out numerical simulations to affirm our analytical findings. Furthermore, we present Maximum Lyapunov exponents (MLEs) and Fractal dimension (FD) numerically in order to justify whether chaos exists in the system or not. At the end, we apply hybrid control strategy to eliminate chaotic trajectories of the system.

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Bifurcation analysis and chaos control in discrete-time eco–epidemiological models of pelicans at risk in the Salton Sea

Cited by 11 publications

References 42 publications

Mutual interference and its effects on searching efficiency between predator–prey interaction with bifurcation analysis and chaos control

Mutual interference and its effects on searching efficiency between predator–prey interaction with bifurcation analysis and chaos control

Bifurcation Analysis and 0-1 Chaos Test of a Discrete T System

Dynamics of a Discrete-Time Chaotic Lü System

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