A nonautonomous model for the effect of environmental toxins on plankton dynamics

Mandal, Arindam; Tiwari, Pankaj Kumar; Samanta, Sudip; Venturino, Ezio; Pal, Samares

doi:10.1007/s11071-020-05480-2

Cited by 32 publications

(6 citation statements)

References 70 publications

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“…The upper-right derivatives of W i (t) along the solution of the system (25) with initial condition (27) are given by,…”

Section: Proof Let (S(t) I(t) Z(t) V(t)) and ( S(t) ĩ(T) Z(t) ṽ(T))mentioning

confidence: 99%

“…Here, we review the behaviors of systems ( 1) and ( 25) by performing numerical simulations. The set of parametric values are adopted from numerous literature sources [27][28][29] and are presented in Table 1.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…Chattopadhyay et al 26 evidenced that toxin substances inhibit zooplankton growth and possess important consequences on phytoplankton‐zooplankton interactions. Recently, Mandal et al 27 studied the influences of seasonal fluctuations of toxin secretion by phytoplankton and input of anthropogenic pollutants on plankton dynamics. They found the nonautonomous system to display globally stable periodic solution while bursting phenomenon is observed for a pair of commensurate excitation frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Effects of toxicity and zooplankton selectivity on plankton dynamics under seasonal patterns of viruses with time delay

Biswas

Tiwari

Pal

2021

Math Methods in App Sciences

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Intricate functional diversities in marine ecosystems often lead to exhibit a variety of dynamical behaviors, including chaos. To bring order into such chaotic situations, the system develops different mechanisms of self‐adaptability. Our present investigation is based on the study of an eco‐epidemiological model for virally infected toxic phytoplankton and zooplankton system. Both healthy and infected phytoplankton are assumed to be exposed to grazer zooplankton with a varying degree of exposure. An extension is made by introducing the fact that viral replication process in a lysis event is mediated by some time lag. To achieve more realistic and explicit outcomes of the existing phenomena correlated with our model, we consider the force of infection and replication of free viruses as seasonally forced. We find that time delay accounts for recurrent stability switching event in the system. The chaotic behavior is observed in the seasonally forced delayed system, which indicates the emergence of harmful blooms. The main motive is to gain a clear insight into the field of synchronization and stabilization of the irregular behaviors of the system. Our investigations suggest that increased strength of toxic compounds exuded by phytoplankton species may suppress the prevalence of chaotic disorder and drives the system into a zooplankton‐free zone. The intensity of selective grazing of zooplankton changes the state of chaos to order and promotes the disease‐free system.

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“…The upper-right derivatives of W i (t) along the solution of the system (25) with initial condition (27) are given by,…”

Section: Proof Let (S(t) I(t) Z(t) V(t)) and ( S(t) ĩ(T) Z(t) ṽ(T))mentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effects of toxicity and zooplankton selectivity on plankton dynamics under seasonal patterns of viruses with time delay

Biswas

Tiwari

Pal

2021

Math Methods in App Sciences

Self Cite

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“…Global dynamics has been analysed with geometrical approach [10]. The effect of environmental toxins has been studied using nonautonomous model [11]. In [12], the analysis has been carried out for the interaction between rugose spiraling whitefly and coconut trees.…”

Section: Introductionmentioning

confidence: 99%

A study on the dynamics of pest population with biocontrol using predator, parasite in presence of awareness

Suganya

Senthamarai

2022

Preprint

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The coconut tree is often mentioned as the “tree of life” due to its immense benefits to the human community ranging from edible products to building materials. Rugose spiraling whitefly (RSW), a natural enemy seems to be a major threat to farmers in bringing up these coconut trees. A mathematical model to study the dynamics of pest population in presence of predator and parasite is developed. The biologically feasible equilibrium points are derived. Local asymptotic stability as well as global asymptotic stability is analyzed at the points. Furthermore, in order to educate farmers on pest control , we have added the impact of awareness programs in the model. The conditions of existence and stability properties of all feasible steady states of this model are analyzed. The result reveals that predator and parasite plays a major role in reducing the immature pest. It also shows that pest control activities through awareness programs further reduces the mature pest population which decreases the egg laying rate which in turn reduces the immature population.

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“…Plankton systems play an important role in the marine ecosystem, which have always attracted attention of ecologists and mathematicians [1][2][3]. Many researchers have established a lot of mathematical models to study the dynamic behaviors of plankton systems [4][5][6][7][8][9][10]. Phytoplankton can be divided into nontoxic phytoplankton and toxic phytoplankton (TPP).…”

Section: Introductionmentioning

confidence: 99%

Stability and Bifurcation for a Delayed Diffusive Two‐Zooplankton One‐Phytoplankton Model with Two Different Functions

Meng

Xiao

2021

Complexity

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In this paper, a diffusion two-phytoplankton one-zooplankton model with time delay, Beddington–DeAnglis functional response, and Holling II functional response is proposed. First, the existence and local stability of all equilibria of such model are studied. Then, the existence of Hopf bifurcation of the corresponding model without diffusion is given by taking time delay as the bifurcation parameter. Next, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are investigated by using the normal form theory and center manifold theorem. Furthermore, due to the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the model is investigated by considering time delay as the bifurcation parameter. The explicit formulas to determine the properties of Hopf bifurcation are given by the method of the normal form theory and center manifold theorem for partial functional differential equations. Finally, some numerical simulations are performed to check out our theoretical results.

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A nonautonomous model for the effect of environmental toxins on plankton dynamics

Cited by 32 publications

References 70 publications

Effects of toxicity and zooplankton selectivity on plankton dynamics under seasonal patterns of viruses with time delay

Effects of toxicity and zooplankton selectivity on plankton dynamics under seasonal patterns of viruses with time delay

A study on the dynamics of pest population with biocontrol using predator, parasite in presence of awareness

Stability and Bifurcation for a Delayed Diffusive Two‐Zooplankton One‐Phytoplankton Model with Two Different Functions

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