Global dynamics of a Holling Type-III two prey–one predator discrete model with optimal harvest strategy

Banerjee, Ritwick; Das, Pritha; Mukherjee, Dhiman

doi:10.1007/s11071-020-05490-0

Cited by 12 publications

(18 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, we have provided evidence for the small changes of fractional orders that can provide a significant impact on the dynamic behavior of the LV system. In the literature, several valuable results such as stability analysis, persistence, permanence, and extinction are studied about the LV system (see [18][19][20][21][22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

“…One of the best strategies is to apply the harvesting force as a control parameter on the particular individuals that are contributing to the damage (see [25]). In the literature (see [26][27][28][29]), many authors studied the LV system with the harvesting effect. From this analysis, we can observe that the immigration and harvesting effects having much influence on the stability of the LV system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Kaviya

Muthukumar

2021

Eur. Phys. J. Plus

View full text Add to dashboard Cite

Aim of this work is to study the four species various fractional-order prey-predator or Lotka-Volterra (LV) system with both immigration and harvesting effects. The existence and uniqueness, uniform boundedness, persistence, permanence, and extinction of this system solution are analyzed. The stability behavior of the system is obtained with the help of the Routh-Hurwitz (RH) stability criterion. The small changes in fractional-order values can produce a significant impact on the stability of the system is confirmed. This work verifies that the small amount of immigration effect can change the dynamic nature of the LV system. Numerical results are given to illustrate the obtained theoretical results of the stability analysis. The bionomic equilibrium points of the system are attained with their feasibility conditions. To get the optimal amount of harvesting effect with the Pontryagin's maximum principle, the harvesting parameter is considered as the control parameter.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Kaviya

Muthukumar

2021

Eur. Phys. J. Plus

View full text Add to dashboard Cite

show abstract

“…we obtain the phase portraits and time series for r 2 = 2, 2.6 and 2.7 respectively in fig. (3). It can be observed that the increase in r 2 leads to the existence of more than one fixed points.…”

mentioning

confidence: 92%

“…After the reintroduction of gray wolves (Canis lupus) in Yellowstone National Park in 1995-1996, the population density of the elk has steadily declined from 17, 000 in 1995 to 5, 800 in 2019 [16]. Several studies have reported trophic cascade effects in YNP after the reintroduction of the wolves [12,13,3]. As the wolves in YNP mainly prey on elks, the reduced density of the elks have led to more availability of forage for the bison, which in turn has a positive effect on the bison population.…”

mentioning

confidence: 99%

“…The paper is organized as follows. In Section (2), a discrete-time two prey one predator is formulated which is followed by the investigation of the existence and local stability of the equilibrium points in Section (3). The conditions of permanence and global asymptotic stability of the interior equilibrium point are obtained in Section (4) and ( 5) respectively.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Effects of fear and anti-predator response in a discrete system with delay

Banerjee

Das

Mukherjee

2022

DCDS-B

Self Cite

View full text Add to dashboard Cite

<p style='text-indent:20px;'>In this paper a discrete-time two prey one predator model is considered with delay and Holling Type-Ⅲ functional response. The cost of fear of predation and the effect of anti-predator behavior of the prey is incorporated in the model, coupled with inter-specific competition among the prey species and intra-specific competition within the predator. The conditions for existence of the equilibrium points are obtained. We further derive the sufficient conditions for permanence and global stability of the co-existence equilibrium point. It is observed that the effect of fear induces stability in the system by eliminating the periodic solutions. On the other hand the effect of anti-predator behavior plays a major role in de-stabilizing the system by giving rise to predator-prey oscillations. Finally, several numerical simulations are performed which support our analytical findings.</p>

show abstract

Dynamics of a discrete one‐predator two‐prey system with Michaelis–Menten‐type prey harvesting and prey refuge

Song,

Li,

Zhu

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we propose and study a discretized one‐predator two‐prey system along with prey refuge and Michaelis–Menten‐type prey harvesting. The interaction among the species is considered as Holling type III functional response. Firstly, existence and local stability of all the fixed points are derived under certain parametric conditions. Furthermore, a special consideration is made to global asymptotic stability of the interior fixed point. Then, we have shown that the system undergoes different types of bifurcations including transcritical bifurcation, flip bifurcation, and Neimark–Sacker bifurcation by using center manifold theorem, bifurcation theory, and normal form method. Also, Feigenbaum's constant of the system is calculated. It is observed that both harvesting and refuge have a stabilizing effect on the system, and the stabilizing effect of harvesting dominates the stabilizing effect of refuge. Of most interest is the finding of coexisting attractors and multistability. In particular, optimal harvesting policy has been obtained by extension of Pontryagin's maximum principle to discrete system. Finally, some intriguing numerical simulations are provided to verify our analytic findings and rich dynamics of the three species system.

show abstract

Global dynamics of a Holling Type-III two prey–one predator discrete model with optimal harvest strategy

Cited by 12 publications

References 25 publications

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Effects of fear and anti-predator response in a discrete system with delay

Dynamics of a discrete one‐predator two‐prey system with Michaelis–Menten‐type prey harvesting and prey refuge

Contact Info

Product

Resources

About