Bifurcation analysis and chaos control of discrete prey–predator model incorporating novel prey–refuge concept

Santra, P. K.; Mahapatra, G. S.; Phaijoo, Ganga Ram

doi:10.1002/cmm4.1185

Cited by 19 publications

(6 citation statements)

References 32 publications

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“…Adding relatively small amounts of prey refuge to the system has no effect on the chaotic behavior of the system. But adding a significant amounts of prey refuge to the system transforms the chaotic behavior into an oscillatory behavior and ultimately into a stable fixed point which resonates with the results in Jana [21] and Santra et al [35] (see Figure 1). The dynamics of system (5) are also significantly influenced by the intrinsic growth rate of prey population.…”

Section: Discussionsupporting

confidence: 86%

Bifurcation and global stability of a discrete prey–predator model with saturated prey refuge

Mondal

Kesh

Mukherjee

2023

Math Methods in App Sciences

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This article aims to describe the qualitative behavior of a discrete‐time prey–predator model including prey refuge. It is assumed that the fraction of prey in refuge is a monotonically increasing but self‐limiting function of prey population. The fixed points of the system and their local stability are investigated. The criteria for Neimark–Sacker bifurcation and period‐doubling bifurcation are presented. The sufficient conditions for global asymptotic stability of the interior fixed point are derived. The chaotic behavior of the system is stabilized by applying a hybrid control strategy. We conclude with a numerical simulation that strengthens our theoretical discussion and provides a way to observe the complex behavior of the system.

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Section: Discussionsupporting

confidence: 86%

Bifurcation and global stability of a discrete prey–predator model with saturated prey refuge

Mondal

Kesh

Mukherjee

2023

Math Methods in App Sciences

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“…Sensitivity and bifurcation analyses have been performed on several models including the Kumar,Basu,Ghosh,Santra,Mahapatra [11] analysis of COVID-19 epidemic model; Santra, Mahapatra and Phaijo [12] bifurcation analysis and chaos control of discrete pre-predator model; Kumar, Basu, Santra, Ghosh and Mahapatra [13] optimal control design; Basu, Kumar, Santra, Mahapatra and Elsadany [14] Covid-19 pandemic's second wave's preventive control strategy; Kumar, Mahapatra, Parshad and Santra [15] model for dengue re-infection; Kumar, Santra and Mahapatra [16] stability and sensitivity analyses of the parameters of a SARS-CoV-2 model; Kumar,Basu, Santra, Elsadany, Elsonbaty, Mahapatraand Al-khedhairi [17] stability and sensitivity analyses of an Omicron variant epidemic's model parameters.…”

Section: Introductionmentioning

confidence: 99%

A Co-infection Model for Monkeypox and HIV/AIDS: Sensitivity and Bifurcation Analyses

Marcus,

Augustine,

Jonathan

2024

JSRR

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Monkeypox can make people very sick. The skin becomes infected with bacteria, thus causing severe skin damage. This can lead to corneal infection with loss of vision, pneumonia, difficulty swallowing, diarrhoea and vomiting leading to harsh malnutrition or dehydration, several organs inflammation or death. HIV-AIDS is a life-threatening and chronic condition. In HIV-infected individuals whose immune systems have been compromised, monkeypox mortality alone may be much higher. The co-infection of monkeypox and HIV/AIDS infections has been studied from a mathematical perspective by constructing a 13-compartment deterministic model. Basic mathematical analyses were performed on the co-infection model and the sub-models. The disease equilibrium points, the non-negativity of solutions, the basic reproduction numbers, the invariant region and the stability patterns. When the basic reproduction number is less than unity, the disease-free equilibrium points of each sub-model are globally asymptomatically stable. Certain calculations were done using the maple 18 programming language. The sensitivity analysis reveals that the parameters of the basic reproduction of the monkeypox sub-model with positive sensitivity indices are the probability of catching the monkeypox virus, the rate of effective contact, the compartment Im ’s coefficient of infection and the monkeypox vaccine’s waning rate, while the parameters of the basic reproduction of the HIV/AIDS sub-model with positive sensitivity indices are the probability of catching HIV virus, the rate effective contact, the compartment Ih ’s coefficient of infection and the compartment Ah ’s coefficient of infection. Via the centre manifold theorem, the bifurcation analysis reveals a forward bifurcation pattern for the monkeypox sub-model and the HIV/AIDS sub-model, and under a certain condition, a critical value of the monkeypox basic reproduction exists such that an effective management and possible elimination of the monkeypox infection would require that the monkeypox basic reproduction number should be kept below unity and above the critical value.

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“…Numerous investigations of the predator-prey relationship with Ivlev-type functional responses have been conducted. Te results suggested that Iviev-type relationships between the species have a number of models in ecological applications, including dynamics in host-parasite models [16], predator-prey models [17][18][19][20][21][22][23][24][25], animal coat patterns [26], and phytoplankton-zooplankton model [27].…”

Section: Introductionmentioning

confidence: 99%

Qualitative Analysis of the Discretization of a Continuous Fractional Order Prey-Predator Model with the Effects of Harvesting and Immigration in the Population

Uddin,

Sohel Rana

2024

Complexity

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This study examines the discrete prey-predator model in the sense of Caputo fractional derivative by incorporating harvesting on the predator population and immigration on the prey population. We establish the topological categories of the model’s fixed points. We show analytically that a fractional order prey-predator model supports both a Neimark–Sacker (NS) bifurcation and a period-doubling (PD) bifurcation under specific parametric circumstances. Using the central manifold and bifurcation theory, we provide evidence for NS and PD bifurcations. It has been discovered that the parameter values and the initial conditions have a significant influence on the dynamical behavior of the fractional order prey-predator model. Furthermore, two chaos management strategies are applied to eliminate the chaos that objectively exists in the model. Finally, numerical simulations are used to demonstrate complicated and chaotic behavior in order to support our theoretical and analytical discussions.

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Bifurcation analysis and chaos control of discrete prey–predator model incorporating novel prey–refuge concept

Cited by 19 publications

References 32 publications

Bifurcation and global stability of a discrete prey–predator model with saturated prey refuge

Bifurcation and global stability of a discrete prey–predator model with saturated prey refuge

A Co-infection Model for Monkeypox and HIV/AIDS: Sensitivity and Bifurcation Analyses

Qualitative Analysis of the Discretization of a Continuous Fractional Order Prey-Predator Model with the Effects of Harvesting and Immigration in the Population

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