Prey–Predator Dynamics with Two Predator Types and Michaelis–Menten Predator Harvesting

Fattahpour, Haniyeh; Nagata, Wayne; Zangeneh, Hamid R. Z.

doi:10.1007/s12591-019-00500-z

Cited by 5 publications

(5 citation statements)

References 47 publications

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“…where Q 6 (X, Y , 𝜉) is high order smooth function of (X, Y ) and the coefficients depend smoothly on 𝜉 1 and 𝜉 2 . To annihilate the term X of the second equation for system (23), taking…”

Section: Bogdanov-takens Bifurcationmentioning

confidence: 99%

“…From the ecological point of view, harvesting of predator species had been given much emphasis to control the predator species and prevent prey species from extinction. As a result, many scholars investigated the dynamic of predator-prey model with a harvesting term in both the prey and predator growth equations, such as constant harvesting [14,15], proportional harvesting [16][17][18], and nonlinear harvesting [19][20][21][22][23][24][25]. But all those only consider the commonly known functional responses.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcation analysis of predator–prey model with Cosner type functional response and combined harvesting

Mulugeta,

Ren,

Yuan

et al. 2024

Math Methods in App Sciences

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In this paper, we consider a predator–prey model with Cosner type functional response and combined harvesting. First, we explore the existence and stability of the equilibria. Then using the center manifold theorem and normal form theory, we investigate codimension one and codimension two bifurcations of the model. The analysis shows that the system has a variety of bifurcation phenomena including transcritical bifurcation, saddle‐node bifurcation, Hopf bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Our findings indicate that the dynamics with harvesting are significantly richer than the system without harvesting. Finally, numerical simulations are provided to support the analytical results.

show abstract

Section: Bogdanov-takens Bifurcationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of predator–prey model with Cosner type functional response and combined harvesting

Mulugeta,

Ren,

Yuan

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…where Q 6 (X, Y, ξ) is high order smooth function of (X, Y ) and the coefficients depend smoothly on ξ 1 and ξ 2 . To annihilate the term X of the second equation for system (23), taking…”

Section: Making Affine Transformationmentioning

confidence: 99%

“…From the ecological point of view, harvesting of predator species had been given much emphasis to control the predator species and prevent prey species from extinction. As a result, many scholars investigated the dynamic of predator-prey model with a harvesting term in both the prey and predator growth equations, such as constant harvesting [14,15], proportional harvesting [16,17,18] and nonlinear harvesting [19,20,21,22,23,24,25]. But all those only consider the comonly known functional responses.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis of predator-prey model with Cosner type functional response and combined harvesting

Yu,

Mulugeta,

Ren

et al. 2024

Preprint

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In this paper, we consider a predator-prey model with Cosner type functional response and combined harvesting. First, we explore the existence and stability of the equilibria. Then using the center manifold theorem and normal form theory, we investigate codimension one and codimension two bifurcations of the model. The analysis shows that the system has a variety of bifurcation phenomena including transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov-Takens bifurcation and homoclinic bifurcation. Our findings indicate that the dynamics with harvesting are significantly richer than the system without harvesting. Finally, numerical simulations are provided to support the analytical results.

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“…The qualitative effect of predator harvesting on the stability of the ecosystem has been investigated extensively [60,62,64,65,66,67]. Chakraborty et al [59] explored a mathematical study with biological ramifications of a predator-prey model with predator effort harvesting.…”

Section: Introductionmentioning

confidence: 99%

Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

Antwi-Fordjour¹,

Parshad²,

Thompson³

et al. 2021

Preprint

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A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We give conditions for the existence of some local and global bifurcations at the coexistence equilibrium. We also show that fear can induce extinction of the prey population from a coexistence zone in finite time. Our numerical simulations reveal that varying the strength of fear of predators with suitable choice of parameters can stabilize and destabilize the coexistence equilibrium solutions of the model. Additionally, we discuss the outcome of introducing a constant harvesting effort to the predator population in terms of changing the dynamics of the system, in particular, from finite time extinction to stable coexistence. Furthermore, we perform extensive numerical experiments to visualize the dynamical behavior of the model and substantiate the results we obtained.

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Prey–Predator Dynamics with Two Predator Types and Michaelis–Menten Predator Harvesting

Cited by 5 publications

References 47 publications

Bifurcation analysis of predator–prey model with Cosner type functional response and combined harvesting

Bifurcation analysis of predator–prey model with Cosner type functional response and combined harvesting

Bifurcation analysis of predator-prey model with Cosner type functional response and combined harvesting

Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

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