The cyclic nature of blooms is a very interesting characteristic of marine plankton ecosystem. Release of toxins by some phytoplanktons has an important role on planktonic interactions and hence on regulating the blooms. A mathematical model describing the phytoplankton-zooplankton interaction with these characteristics is studied. The time needed for liberation of toxins by phytoplanktons is considered. To account for the spatial heterogeneity of an aquatic environment, diffusivity of different plankton populations is also incorporated into the system. Stability and bifurcation behaviour of different steady states are analysed. © Springer 2005.

B MUKHOPADHYAY

R BHATTACHARYYA

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Journal of Biological Physics

We present a nonlinear SEIS epidemic model which incorporates distinct incidence rates for the exposed and the infected populations. The model is analyzed for stability and bifurcation behavior. To account for the realistic phenomenon of non-homogeneous mixing, the effect of diffusion on different population subclasses is considered. The diffusive model is analyzed using matrix stability theory and conditions for Turing bifurcation derived. Numerical simulations are performed to justify analytical findings. © 2007 Elsevier Ltd. All rights reserved.

Nonlinear Analysis: Real World Applications

Analysis of a spatially extended nonlinear SEIS epidemic model with distinct incidence for exposed and infectives

The present paper studies the naturally observed phenomenon of population fluctuation in the context of a minimal plankton model. The analysis of the basic model reveals asymptotic stable behavior that is unable to explain any kind of population outburst. We introduce the nonuniform spatial distribution of plankton by considering physical diffusion of the species concerned. The resulting reaction-diffusion equation model is first analyzed with constant diffusivity and then with variable diffusivity for the Zooplankton. The model with variable diffusivity is analyzed by using Floquet theory. In both cases, the model is seen to exhibit stable behavior. Finally, we study another characteristic feature of any ecological population, namely, environmental fluctuations. We achieve this by perturbing the growth rate of phytoplankton and death rate of Zooplankton by using colored noise. The resulting model is analyzed by evaluating the spectral density functions. It is observed tha,t the stochastic model can generate a large fluctuation in population concentration for high amplitude driving forces. © World Scientific Publishing Company.

Advances in Complex Systems

Modeling fluctuations in a minimal plankton model: Role of spatial heterogeneity and stochasticity

We analyze a mathematical model of predator-prey interaction where the prey population is infected with a viral disease. Infection in the prey population is assumed to follow standard incidence. The dynamical behavior of the system is studied in terms of stability aspects. To model the gestation lag of the predator species and the spatially heterogeneous characteristics of an ecological population, we incorporate the concept of diffusionally coupled delay into the system. The bifurcation behavior of the delayed homogeneous system is studied. The existence of traveling wave solutions for the delay diffusion model is established. Numerical simulations are performed to justify analytical findings.

JOURNAL OF MECHANICS IN MEDICINE AND BIOLOGY

Spatiotemporal dynamics of an ecoepidemiological model with standard incidence

The present paper deals with a nutrient-plankton model in an aquatic environment in the context of phytoplankton bloom. Toxin producing phytoplanktons are assumed to play the key role. To account for the toxication effect of the allelopathic phytoplankton, a type-IV functional response is used to model zooplankton grazing. The main aim of the study is to analyze the role, zooplankton grazing plays, in determining the dynamics of the system. Stability and bifurcation behavior of the different equilibrium points of the ODE model is studied. It has been observed that under certain parameter restrictions, extinction of one or both plankton population can occur. The model system is seen to exhibit oscillatory behavior around the equilibrium point of co-existence for a critical value of zooplankton grazing rate. A spatial extension of the model is considered and analyzed for diffusion-driven instability as well as stability. For the diffusive model also, it is found that diffusion-driven instability takes place when the grazing rate of zooplankton lies within an interval. The analysis also revealed that for sufficiently low diffusivity of phytoplankton and high value of half-saturation constant in zooplankton predation function, the diffusive system exhibit asymptotically stable behavior which signifies disappearance of the phenomenon of bloom formation for the diffusive model. Cross-diffusion of zooplankton under the influence of allelopathic phytoplankton is incorporated into the spatial model. Using matrix stability approach, the cross-diffusive model is analyzed and criteria for Turing bifurcation derived. Numerical simulations are performed to justify analytical findings. © 2006 Elsevier B.V. All rights reserved.

Ecological Modelling

Modelling phytoplankton allelopathy in a nutrient-plankton model with spatial heterogeneity

Mathematical Medicine and Biology

A delay differential equation model on harmful algal blooms in the presence of toxic substances

Estuaries

The Decline and Recovery of a Persistent Texas Brown Tide Algal Bloom in the Laguna Madre (Texas, USA)

Interdisciplinary Applied Mathematics Diffusion and Ecological Problems: Modern Perspectives

Introduction: The Mathematics of Ecological Diffusion

Bulletin of Mathematical Biology

Zooplankton Mortality and the Dynamical Behaviour of Plankton Population Models

Sarsia

Repression of copepod feeding and fecundity by the toxic haptophytePrymnesium patelliferum

A delay-diffusion model of marine plankton ecosystem exhibiting cyclic nature of blooms

Journal	Data powered by TypesetJournal of Biological Physics
Publisher	Data powered by TypesetSPRINGER
ISSN	0092-0606
Open Access	Yes