Complex dynamics of delay-induced plankton–fish interaction exhibiting defense

Thakur, Nilesh Kumar; Ojha, Archana

doi:10.1007/s42452-020-2860-7

Cited by 15 publications

(18 citation statements)

References 46 publications

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“… 2015 ). Recently, Thakur and Ojha ( 2020b ) have investigated a three-tier delayed plankton-fish model system and considered the effect of delay on the extinction behavior of fish. They obtained that the increasing value of time delay helps to stabilize the fish dynamics after the extinction through the double Hopf-bifurcation phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

Thakur

Srivastava

Ojha

2021

Iran J Sci Technol Trans Sci

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Section: Introductionmentioning

confidence: 99%

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

Thakur

Srivastava

Ojha

2021

Iran J Sci Technol Trans Sci

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“…In particular, predator-prey models are used when describing plankton-fish interaction (see, for example, [9][10][11][12][13][14]). Taking into account a model proposed in [14], in the present paper, we study the model of the following form:…”

Section: Introductionmentioning

confidence: 99%

“…which can be also considered a model of plankton-fish interaction (note that, in [14], it was considered the case that τ 2 = 0, but nonlinear terms had a more general form). In this system, x(t) is the amount of phytoplankton, y(t) is the amount of zooplankton, and z(t) is the number of fish.…”

Section: Introductionmentioning

confidence: 99%

“…It is well known that a solution to the initial value problems (1) and (2) exists and is unique. Moreover, by analogy with [14], it is not difficult to show that the solution is defined on the entire right half-axis {t > 0}, has non-negative components, and each component of the solution is a bounded function. In other words, there exist constants M 1 , M 2 , M 3 > 0 such that, for all t > 0, the inequalities are valid…”

Section: Introductionmentioning

confidence: 99%

“…In [14], it was noted that, for τ 2 = 0, a sufficient condition for the asymptotic stability of this equilibrium point is the condition…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction

Skvortsova¹

2021

Mathematics

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We consider a system of differential equations with two delays describing plankton–fish interaction. We analyze the case when the equilibrium point of this system corresponding to the presence of only phytoplankton and the absence of zooplankton and fish is asymptotically stable. In this case, the asymptotic behavior of solutions to the system is studied. We establish estimates of solutions characterizing the stabilization rate at infinity to the considered equilibrium point. The results are obtained using Lyapunov–Krasovskii functionals.

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Complex dynamics induced by multiple gestation delays in a Leslie–Gower‐type system with competitive interference

Ojha

Thakur

2023

Math Methods in App Sciences

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The dynamics of food consumption by higher trophic level is complicated as its availability, choice, and consequently their development. The top predator interference has a strong influence on the dynamic structure of the tritrophic food chain system. The proposed article deals with the characteristic features of a three‐tire modified Leslie–Gower model with a one‐prey two‐predator system with the assumption of multiple gestation delays. The intermediate predator of the food chain is taken as a specialist type, whereas the growth of top predator is assumed by sexual reproduction. Two different response functions named Monod–Haldane (M‐H) and Beddington–DeAngelis (B‐D) are considered for the modeling of system dynamics. The population densities of intermediate and top predators are assumed to be affected by two different gestation delays. The boundedness and positive equilibria and their stability conditions are examined theoretically for the delay‐free system. The local and global stability conditions of the delayed system are also determined. With the help of normal form theory and central manifold arguments, the properties of bifurcating periodic solutions are carried out. The numerical computation is performed to validate our analytical findings that show the different dynamical outcomes such as periodic and chaotic dynamics. The Hopf‐bifurcation scenario for different parameters of the model system is well studied. Further, the stability behavior of multiple delays for the different cases is investigated. The system shows chaotic behavior when the gestation delay of intermediate predators is large enough. It is also observed that the top predator density is highly fluctuating through the creation of chaos by the inclusion of time delay. Finally, the time delay destabilizing effect is noticed for three‐way interactions among prey, intermediate predator, and top predator, highlighting its significance in chaotic dynamics.

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Complex dynamics of delay-induced plankton–fish interaction exhibiting defense

Cited by 15 publications

References 46 publications

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

Dynamical Study of an Eco-Epidemiological Delay Model for Plankton System with Toxicity

Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction

Complex dynamics induced by multiple gestation delays in a Leslie–Gower‐type system with competitive interference

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