Modeling and analysis of a fractional-order prey-predator system incorporating harvesting

Mandal, Manotosh; Jana, Soovoojeet; Nandi, Swapan Kumar; Kar, Tapan Kumar

doi:10.1007/s40808-020-00970-z

Cited by 13 publications

(5 citation statements)

References 34 publications

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“…Scholars discovered that physical phenomena in nature can be depicted more accurately by fractional-order models in comparison with classical integer-order ones [8]. Recently, quite a few researchers introduced fractional calculus into the predator-prey model and constructed fractional predator-prey models, for example, design and control of various ecological models [9][10][11], secure communication [12,13], system control [14,15], and so on. Furthermore, modelling and control based on the theory of the fractional calculus of complex systems can greatly enhance the capability of discrimination, design, and control for dynamic models since fractional calculus possesses infinite memory and more degrees of freedom [16].…”

Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a fractional-order predator-prey network with feedback control strategy

Zhang,

Fei,

et al. 2024

Preprint

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To procure the desirable dynamical performance, some control strategies have currently burgeoned into essential study activities in fractional-order intricate systems with delays. This paper examines the bifurcation control problem of a delayed fractional-order predator-prey model in accordance with an enhancing feedback controller. Initially, the bifurcation points of devised model are precisely figured out via theoretic derivation by taking time delay as a bifurcation parameter. Then, a range of comparative analysis on the influence of bifurcation control are numerically discussed including enhancing feedback, dislocated feedback and eliminating feedback approaches. It witnesses that the stability performance of the proposed model can be immensely heightened by the enhancing feedback approach. The feasibility of the devised scheme are nicely verified by means of numerical simulations. Our results provide important theoretical guidance for the application of enhancing feedback control scheme in engineering.

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Section: Introductionmentioning

confidence: 99%

Mathematical analysis of a fractional-order predator-prey network with feedback control strategy

Zhang,

Fei,

et al. 2024

Preprint

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“…where ϱ ∈ (0, 1]. Since the left-hand dimensions of two equations of model ( 2) are time −ϱ and the right-hand dimensions of the two equations of model ( 2) are time −1 , based on the idea of Mandal et al [25], we modify the dimension of model ( 2) and obtain the following expression:…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

Zhang,

2024

Fractal Fract

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Fractional-order differential equations have been proved to have great practical application value in characterizing the dynamical peculiarity in biology. In this article, relying on earlier work, we formulate a new fractional oxygen–plankton model with delay. First of all, the features of the solutions of the fractional delayed oxygen–plankton model are explored. The judgment rules on non-negativeness, existence and uniqueness and the boundedness of the solution are established. Subsequently, the generation of bifurcation and stability of the model are dealt with. Delay-independent parameter criteria on bifurcation and stability are presented. Thirdly, a hybrid controller and an extended hybrid controller are designed to control the time of onset of bifurcation and stability domain of this model. The critical delay value is provided to display the bifurcation point. Last, software experiments are offered to support the acquired key outcomes. The established outcomes of this article are perfectly innovative and provide tremendous theoretical significance in balancing the oxygen density and the phytoplankton density in biology.

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“…The significance of this model lies in the in-depth understanding and interpretation of the food chain and food web structure in the ecosystem, as well as the interrelationship between prey and predators. Jana et al [16], Mandal et al [21] used mathematical models with the help of ordinary differential equations to describe the prey-predator system and made significant progress. When there are insects or other pests in the system that cause harm to crops, horticultural crops, livestock, human health, or other ecosystems, we call them pests.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of an infected prey–predator model with fear effect

Qiu,

Zhang,

Hou

2024

NAMC

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In this paper, we propose and analyze a prey–predator model with the functional response of Beddington–DeAngelis and the fear effect that have infection only in prey populations. We determine existence criteria of several equilibria, and the stability at different equilibria are presented. We exert pesticide control over prey and additional food control over predators, the optimal control is obtained by the Pontryagin maximum principle. We confirm that adding controls to the predator and prey yields better results. Further we enrich our analysis with the inclusion of the existence and uniqueness of the optimal control. Finally, some numerical results to illustrate our analysis are presented.

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Modeling and analysis of a fractional-order prey-predator system incorporating harvesting

Cited by 13 publications

References 34 publications

Mathematical analysis of a fractional-order predator-prey network with feedback control strategy

Mathematical analysis of a fractional-order predator-prey network with feedback control strategy

Bifurcation Exploration and Controller Design in a Fractional Oxygen–Plankton Model with Delay

Optimal control of an infected prey–predator model with fear effect

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