Modeling and analysis of inhibitory effect in plankton–fish model: Application to the hypertrophic Swarzedzkie Lake in Western Poland

Raw, S. N.; Mishra, Pavan Kumar

doi:10.1016/j.nonrwa.2018.09.026

Cited by 21 publications

(12 citation statements)

References 28 publications

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“…which considers the defense of prey against predators and known as Holling IV response [8]. A simplified version without handling time (i.e., t h = 0 in (1.1) f (u) = au m + bu 2 of model (1.1) is proposed and applied in order to investigate group defense behavior in various predator-prey models [9][10][11]. On the basis of some field observations, it is reported that this nonmonotonic function is best suitable functional response for anti-predation modeling [8,12].…”

Section: Introductionmentioning

confidence: 99%

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Drivers of pattern formation in a predator–prey model with defense in fearful prey

Mishra

Tiwari

2021

Nonlinear Dyn

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Existence of predator is routinely used to induce fear and anxiety in prey which is well known for shaping entire ecosystem. Fear of predation restricts the development of prey and promotes inducible defense in prey communities for the survival. Motivated by this fact, we investigate the dynamics of a Leslie–Gower predator prey model with group defense in a fearful prey. We obtain conditions under which system possess unique global-in-time solutions and determine all the biological feasible states of the system. Local stability is analyzed by linearization technique and Lyapunov direct method has been applied for global stability analysis of steady states. We show the occurrence of Hopf bifurcation and its direction at the vicinity of coexisting equilibrium point for temporal model. We consider random movement in species and establish conditions for the stability of the system in the presence of diffusion. We derive conditions for existence of non-constant steady states and Turing instability at coexisting population state of diffusive system. Incorporating indirect prey taxis with the assumption that the predator moves toward the smell of prey rather than random movement gives rise to taxis-driven inhomogeneous Hopf bifurcation in predator–prey model. Numerical simulations are intended to demonstrate the role of biological as well as physical drivers on pattern formation that go beyond analytical conclusions.

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Section: Introductionmentioning

confidence: 99%

“…10) with u(0) = 2.5, v(0) = 3.0. We present Figs.2 and 4as the evidence of Hopf bifurcation at b = b .…”

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confidence: 99%

Drivers of pattern formation in a predator–prey model with defense in fearful prey

Mishra

Tiwari

2021

Nonlinear Dyn

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“…So, the study of the dynamics of Fish in the presence of Phytoplankton and Zooplankton is very much important research topics. There exists very few research articles [4,14,21,22,27,36] in the literature on Phytoplankton-Zooplankton-Fish dynamics. But till now, several unexplored dynamics of Phytoplankton-Zooplankton-Fish to be investigated.…”

Section: Introductionmentioning

confidence: 99%

A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

Panja¹,

Jana²

2020

Nep J. Math. Sci.

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In this investigation, a predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed. In the absence of Zooplankton and Fish, it is assumed that Phytoplankton grows logistically. It is assumed that Zooplankton consumes Phytoplankton and Fish consumes Phytoplankton as well as Zooplankton. Holling type I & II functional responses have been considered to formulate the our proposed model. It is considered that Phytoplankton releases some toxin in the aquatic environment which makes some death in Zooplankton population. Quadratic harvesting is considered on Fish species. Boundedness of the solution of our proposed model has also been studied. Local stability of the system around each equilibrium point has been investigated. Also, the global stability of the interior equilibrium point has been studied. Existence condition of Hopf bifurcation of our proposed system has been studied. It is found that half saturation constant (α) can change the system dynamics. It is also found that the harvesting rate of Fish (E) and consumption rate of Zooplankton (γ1) has a significant role in the stability of the system. Again, it is found that the harvesting of Fish species will be increased if the selling price of Fish (p) and the annual discount (δ1) of Fish production cost increases. It is also found that the optimal harvesting rate of Fish decreases due to the increase of cost (c) of harvesting of Fish. Finally, some numerical simulation results have been presented to verify our analytical findings.

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“…Xiao and Zhu [24] studied stability and periodic oscillations via Hopf bifurcation in a non-monotonic predator-prey model exhibiting group defense. Predator-prey models of non-monotonic functional response are abundant in literature and are extensively studied by several scientists [11,18,23,25,26].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Study About a Predator–Prey Model with Anti-predator Behavior

Raw

Mishra

Tiwari

2020

Int. J. Appl. Comput. Math

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Species use their defense mechanisms to fight, kill or escape from predators. Each species shows its unique defense mechanism to avoid the predation. In this paper, we propose and analyze a three species predator-prey system with group defense mechanism. Conditions for boundedness and positivity of equilibrium points have been discussed. We establish conditions for stability of positive equilibrium points and periodic solutions via Hopf-bifurcation. The predator-prey system is numerically studied with the help of phase portrait, time evolution and bifurcation diagrams. Lyapunov exponent and sensitivity analysis ensure the chaotic behaviour of the model system. Period doubling and period halving bifurcations show dynamical complexities of the food chain system. This study suggests that the repercussion of better group defense by the intermediate predator is able to produce chaos in food chain models.

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Modeling and analysis of inhibitory effect in plankton–fish model: Application to the hypertrophic Swarzedzkie Lake in Western Poland

Cited by 21 publications

References 28 publications

Drivers of pattern formation in a predator–prey model with defense in fearful prey

Drivers of pattern formation in a predator–prey model with defense in fearful prey

A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

Mathematical Study About a Predator–Prey Model with Anti-predator Behavior

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