An investigation of delay induced stability transition in nutrient-plankton systems

Thakur, Nilesh Kumar; Ojha, Archana; Tiwari, Pankaj Kumar; Upadhyay, Ranjit Kumar

doi:10.1016/j.chaos.2020.110474

Cited by 21 publications

(6 citation statements)

References 59 publications

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“…It is observed that the model is more comprehensive by taking account of the zooplankton population, and rich dynamical behaviors have been presented in [3,8,10,26], such as uniform persistence, Turing bifurcation, and global Hopf bifurcation. However, these models do not investigate the joint effect of spatial diffusion and time delay.…”

Section: Discussionmentioning

confidence: 99%

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Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction‐Diffusion Nutrient‐Phytoplankton Model

Zhuang

Liu

2021

Complexity

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In this paper, we study a reaction-diffusion nutrient-phytoplankton model with nutrient recycling delay and toxin-producing phytoplankton. For the delay-free case, we prove that the release rate of toxic chemicals by the toxin-producing phytoplankton can destabilize the system and cause periodic oscillation. For the time-delayed case, we observe that nutrient recycling delay may bring about stability switches and Hopf bifurcation. Moreover, we derive the formula for determining the direction and stability of the bifurcating periodic solutions. Finally, we give some numerical simulations to support the theoretical analyses.

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Section: Discussionmentioning

confidence: 99%

“…It is found that inclusion of nutrient recycling enhances the chances of recurring bloom dynamics. After that, some expanded models were investigated by incorporating zooplankton population in [7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction‐Diffusion Nutrient‐Phytoplankton Model

Zhuang

Liu

2021

Complexity

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“…Many research articles have focused on the study of delay induced nutrient-plankton model system [7]. Thakur et al [29] explored a nutrient-plankton system with delay to review the impact of phytoplankton toxicity, which causes the extra morality of zooplankton in the system dynamics and found https://www.journals.vu.lt/nonlinear-analysis chaotic oscillations through stability switching for the high value of toxin maturation delay. Singh et al [25] studied a diffusive nutrient-plankton system and observed that the liberation of toxins stabilizes/destabilizes the system in the presence of time delay.…”

Section: Introductionmentioning

confidence: 99%

Delay-induced nutrient recycling in plankton system: Application to Sundarban mangrove wetland

Singh,

Ojha,

Thakur

et al. 2024

NAMC

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The paper discusses the nutrient–plankton system with effect of time delay in nutrient recycling and toxin determined function response (TDFR). The designed model system explores the delay-induced system dynamics. We present the local stability analysis of interior equilibrium points in absence as well as in presence of time delay. Further, the direction of Hopf bifurcation is obtained. We perform the numerical computation and observe that time delay in nutrient recycling can generate the periodic solution in a stable nutrient–plankton system. Some other essential parameters, such as input concentration of nutrients and natural removal rate of nutrients, also regulate the dynamical system. The system shows Hopf and double-Hopf bifurcation in the presence of time delay. Our study shows that the delay in the nutrient recycling causes instability transition phenomenon. The delay-induced nutrient recycling and different input concentrations of nutrients can regulate the estuarine system. Finally, the stability switching is observed for delayed system.

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“…Even a simple delay-induced system can generate chaos [11,12]. The inclusion of time delay helps to study the long-term behavior and demographic processes of the interacting population of the ecosystem [13,14]. One of such fascinating situation arises owing to time delay is the appearance of two critical values in the system, and this phenomenon is known as double Hopf bifurcation [15].…”

Section: Introductionmentioning

confidence: 99%

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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An investigation of delay induced stability transition in nutrient-plankton systems

Cited by 21 publications

References 59 publications

Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction‐Diffusion Nutrient‐Phytoplankton Model

Stability Switches and Hopf Bifurcation Induced by Nutrient Recycling Delay in a Reaction‐Diffusion Nutrient‐Phytoplankton Model

Delay-induced nutrient recycling in plankton system: Application to Sundarban mangrove wetland

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

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