Order to chaos and vice versa in an aquatic ecosystem

Mandal, Sandip; Ray, Santanu; Roy, Simanta; Jørgensen, Sven Erik

doi:10.1016/j.ecolmodel.2006.03.020

Cited by 24 publications

(10 citation statements)

References 36 publications

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“…Both Hastings and Powell [9] and Chattopadhyay and Sarkar [11] have used half saturation constant of zooplankton as key parameter in their model to study the system dynamics from order to chaos. Mandal et al [24] studied the modified Hastings and Powell model by considering different body sizes of zooplankton and accordingly the growth rate and half saturation constant have changed. This interaction is represented by the following system of a simple preyspecialist predator -specialist predator interaction.…”

Section: Model Systemsmentioning

confidence: 99%

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Dynamical Complexity in Some Ecological Models: Effects of Toxin Production by Phytoplankton

Upadhyay

Naji

Kumari

2007

NAMC

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We investigate dynamical complexities in two types of chaotic tri-trophic aquatic food-chain model systems representing a real situation in the marine environment. Phytoplankton produce chemical substances known as toxins to reduce grazing pressure by zooplankton [1]. The role of toxin producing phytoplankton (TPP) on the chaotic behavior in these food chain systems is investigated. Holling type I, II, and III functional response forms are considered to study the interference between phytoplankton and zooplankton populations in the presence of toxic chemical. Our study shows that chaotic dynamics is robust to changes in the rates of toxin release as well as the toxin release functions. The present study also reveals that the rate of toxin production by toxin producing phytoplankton plays an important role in controlling oscillations in the plankton system. The different mortality functions of zooplankton due to toxin producing phytoplankton have significant influence in controlling oscillations, coexistence, survival or extinction of the zooplankton population. Further studies are needed to ascertain if this defence mechanism suppresses chaotic dynamics in model aquatic systems.

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Section: Model Systemsmentioning

confidence: 99%

“…This interaction is represented by the following system of a simple preyspecialist predator -specialist predator interaction. The basic mathematical model can now be represented by a set of three ordinary differential equations describing the rate of change of TPP, zooplankton and fish population over time [11,24] given by…”

Section: Model Systemsmentioning

confidence: 99%

Dynamical Complexity in Some Ecological Models: Effects of Toxin Production by Phytoplankton

Upadhyay

Naji

Kumari

2007

NAMC

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“…Nonetheless, such models need to be analyzed in detail since those models are found to be efficient to explain more exotic process of food web. At the begining of nineties, Hastings and Powell (HP) [6] produced an example of a chaotic system in a three species food chain modelled with type II functional responses and found to be most widely accepted [7][8][9][10][11][12][13] for defining the movement of aquatic ecosystem from its equilibrium state to chaotic states.…”

Section: Introductionmentioning

confidence: 99%

Qualitative behavior of three species food chain around inner equilibrium point: spectral analysis

Mandal

Panja

Ray

et al. 2019

NAMC

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This work deals with analytical investigation of local qualitative temporal behavior around inner equilibrium point of a model for three species food chain, studied earlier by Hastings and Powel and others. As an initial step towards the spectral analysis of the model, the governing equations have been split into linear and nonlinear parts around arbitrary equilibrium point. The explicit parameter dependence of eigenvalues of Jacobi matrix associated to the linear part have been derived. Analyzing these expressions in conjunction with some pedagogical analysis, a lot of predictions on stable, unstable or chaotic change of species have been highlighted. Agreement of predictions of this work with available numerical or semi-analytical studies suggest the utility of analytical results derived here for further investigation/analysis of the model as desired by earlier works.

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“…To assess the ecological implications of chaotic dynamics in different natural system, it is important to explore changes in the dynamics when structural assumptions of the system are varied. One such approach to the study of the dynamics of marine ecological community is its food web and the coupling of interacting species with each other [2]. Upadhyay and Rai [3] provided new examples of a chaotic population system in a simple tri-trophic food chain with Holling type II functional response.…”

Section: Introductionmentioning

confidence: 99%

Chaotic Dynamics in a Three Species Aquatic Population Model with Holling Type II Functional Response

Upadhyay

2008

NAMC

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A three-trophic model for marine community is proposed and investigated by means of numerical bifurcation analysis. The proposed model based on a modified version of the Leslie-Gower scheme, incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We investigate the dynamical behavior of the model system by considering the Holling type II functional response of toxin liberation process. Bifurcation diagram and two-dimensional parameter scan suggest that chaotic dynamics is robust to variations in toxin production by phytoplankton. Our study suggests that toxic substances released by TPP population may act as bio-control by changing the state of chaos to order. The mutual interference also induces chaos and acts as both stabilizing and destabilizing factors.

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Order to chaos and vice versa in an aquatic ecosystem

Cited by 24 publications

References 36 publications

Dynamical Complexity in Some Ecological Models: Effects of Toxin Production by Phytoplankton

Dynamical Complexity in Some Ecological Models: Effects of Toxin Production by Phytoplankton

Qualitative behavior of three species food chain around inner equilibrium point: spectral analysis

Chaotic Dynamics in a Three Species Aquatic Population Model with Holling Type II Functional Response

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