Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach

Das, Kalyan; Srinivas, M. N.; Madhusudanan, V.; Pinelas, Sandra

doi:10.3390/mca24010022

Cited by 7 publications

(14 citation statements)

References 24 publications

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“…(4). The parameter values used in the simulations were as follows: 12 = 0.3 [22], 12 = 1.2, 1 = 2, 2 = 3.6, = = 0.5 [16], = = 0.25 [16], 1 = 0.004, 2 = 0.002 and = 1.5 except when stated otherwise. The choice of parameter values was for simulations purpose only.…”

Section: Numerical Simulation Resultsmentioning

confidence: 99%

Modeling the Phenomenon of Xenophobia in Africa

Gweryina

Madubueze

Ogaji

2021

J. Math. Fund. Sci.

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In this study, we applied the principle of a competitive predator-prey system to propose a prey-predator-like model of xenophobia in Africa. The boundedness of the solution, the existence and stability of equilibrium states of the xenophobic model are discussed accordingly. As a special case, the coexistence state was found to be locally and globally stable based on the parametric conditions of effective group defense and anti-xenophobic policy implementation. The system was further analyzed by Sotomayor’s theory to show that each equilibrium point bifurcates transcritically. However, numerical proof showed period-doubling bifurcation, which makes the xenophobic situation more chaotic in Africa. Further numerical simulations support the analytical results with the view that tolerance, group defense and anti-xenophobic policies are critical parameters for the coexistence of foreigners and xenophobes.

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Section: Numerical Simulation Resultsmentioning

confidence: 99%

Modeling the Phenomenon of Xenophobia in Africa

Gweryina

Madubueze

Ogaji

2021

J. Math. Fund. Sci.

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“…then A 1 < 0 and A 0 < 0, which satisfy Descartes rule of sign to have a unique positive real root S * of (6). Moreover, by the above condition (7), I * and P * also feasibles. Hence E * (S * , I * , P * ) is feasible when (7) is satisfied.…”

Section: Equilibria and Their Feasibilitymentioning

confidence: 96%

An ecoepidemic model with healthy prey herding and infected prey drifting away

Rahman¹,

Pramanik²,

Venturino³

2023

NAMC

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We introduce here a predator–prey model where the prey are affected by a disease. The prey are assumed to gather in herds, while the predators are loose and act on an individualistic basis. Therefore their hunting affects mainly the prey individuals occupying the outermost positions in the herd, which is modeled via a square root functional response. The conditions of boundedness and uniform persistence are established. Stability and bifurcation analysis of all feasible equilibrium are carried out. Conditions on the model parameters for the possible existence of limit cycles are derived, global stability analysis is also shown in proper choice of suitable Lyapunov function. Numerical simulation of the various bifurcations validate the theoretical results. It is found that the system ultimate behavior depends mainly on two crucial parameters, the force of infection and predator average handling time. A discussion of the biological significance of the investigation concludes the paper.

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“…The global stability behavior of the system of equations at the coexistent equilibrium point is investigated using the Lyapunov stability theorem [41]. Time derivative given by Equation 8is negative definite if * < ( − 1) .…”

Section: Global Stability Analysismentioning

confidence: 99%

Evolution of COVID-19 Disease Using a One Prey-Two Predator Mode

Ambegedara

Konpola²,

Gunasekara³

et al. 2021

AIT

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Mathematical modeling is used to understand the dynamics of transmission of infectious diseases such as COVID-19, SARS, Ebola, and Dengue among populations. In this work, a one prey-two predator model has been developed to understand the underlying dynamics of COVID-19 disease transmission. We considered the infected, recovered, and death populations with the fact that an infected person can be transformed into the recovered or death group assuming that the infected ones are the prey, and the other two populations are the two predators in the one prey-two predator model. It was found that the proposed model has four equilibrium points; the vanishing equilibrium point ( ), recovered and death-free equilibrium point ( ), recovered population-free equilibrium point ( ), and the death-free equilibrium point ( ). Stability analysis of the equilibrium points shows that except all the other equilibrium points are locally asymptotically stable. Global asymptotic stability of the recovered population-free equilibrium point and death-free equilibrium point are also analyzed. Moreover, the existence and uniqueness of the solution were proved. The parameters for the model are estimated from a data set that consists of the total number of infected, recovered, and dead populations worldwide in the year 2020 using the Nelder-Mead optimization method. When the time approaches infinity, the infected population converges to a constant value, the recovered population declines and reaches zero, and the death population attains a constant value. However, some modifications to the system are needed. In future work, measures such as health precautions, vaccinations are needed to be considered for the formulation of the mathematical model.

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Mathematical Analysis of a Prey–Predator System: An Adaptive Back-Stepping Control and Stochastic Approach

Cited by 7 publications

References 24 publications

Modeling the Phenomenon of Xenophobia in Africa

Modeling the Phenomenon of Xenophobia in Africa

An ecoepidemic model with healthy prey herding and infected prey drifting away

Evolution of COVID-19 Disease Using a One Prey-Two Predator Mode

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