Nonlinear dynamics and chaotic and complex systems constitute some of the most fascinating developments of late twentieth century mathematics and physics. The implications have changed our understanding of important phenomena in almost every field of science, including biology and ecology. This article investigates complexity and chaos in the spatiotemporal dynamics of aquatic ecosystems. The dynamics of these biological communities exhibit an interplay between processes acting on a scale from hundreds of meters to kilometers, controlled by biology, and processes acting on a scale from dozens to hundreds of kilometers, dominated by the heterogeneity of hydrophysical fields. We focus on how biological processes affect spatiotemporal pattern formation. Our results show that modeling by reaction-diffusion equations is an appropriate tool for investigating fundamental mechanisms of complex spatiotemporal plankton dynamics, fractal properties of planktivorous fish school movements, and their interrelationships.

http://www.math.le.ac.uk/PEOPLE/sp237/Medvinsky_etal_SIAM-02.pdf

Spatiotemporal Complexity of Plankton and Fish Dynamics

Nutrient-phytoplankton-zooplankton (NPZ) models have been in use in oceanography for at least three decades, and are still a common research tool. Given the discoveries of the last two decades, particularly concerning the role of bacteria in the plankton, there are questions as to whether NPZ models can still be supported as a useful tool in planktonic research. Here I review the construction of NPZ models, and some of the physical platforms they have been coupled to. I then discuss the applications of NPZ-physical models, and conclude that they still constitute an important and viable research tool, provided that the questions being explored are clearly stated.

http://faculty.petra.ac.id/dwikris/docs/cvitae/docroot/html/www.terrapub.co.jp/journals/JO/pdf/5802/58020379.pdf

NPZ Models of Plankton Dynamics: Their Construction, Coupling to Physics, and Application

http://repository.ias.ac.in/7491/1/355.pdf

Toxin-producing Plankton May Act as a Biological Control for Planktonic Blooms—Field Study and Mathematical Modelling

Zooplankton mortality and the dynamical behaviour of plankton population models.

Zooplankton mortality in plankton population models is often represented by the so-called closure term. Recently, much attention has been paid to the choice of functional form used for the closure term, primarily due to the influential paper by Steele and Henderson (J. Plankton Res., 14, 157-172, 1992). Here we reveal an inconsistency in the normalization of Steele and Henderson's models, and show that unforced short-term oscillations (limit cycles) can occur when a quadratic closure term is used. Furthermore, we contradict the hypothesis regarding the relationship between nutrient steady- state values and the choice of closure term: using the seven-component plankton model of Fasham (The Global Carbon Cycle, Heimann,M. (ed.), pp. 457-504, 1993) with four alternative closure terms, we find the nutrient value to depend more upon the choice of parameter values than on the choice of closure term. However, our results agree with and strengthen the general conclusion of Steele and Henderson's work: that the choice of closure term can strongly influence the dynamics of models.

The role of higher predation in plankton population models

The thermal runaway and eventual ignition of flammable fluids in lagging materials has occurred with sufficient frequency for there to be considerable awareness of this problem in the process engineering industry. Earlier (mainly spatially invariant) models are here modified to include the important effect of diffusion. The aim is to identify boundaries in parameter space where ignition will or will not occur. In this paper, a model of the three main contributing quantities (temperature, fuel and oxygen concentration) is considered which includes exothermic oxidation and endothermic evaporation/desorption processes and primarily centres on the energy balance equation. The shape of the ignition boundary is found to depend crucially on a key value of the ratio of thermal diffusion to mass diffusion of oxidant (inverse Lewis number). The critical value of this ratio is in fact size-dependent and beyond a certain value, ignition will be suppressed.

Spatial effects in the thermal runaway of combustible fluids in insulation materials

The autoignition of flammable fluids in lagging materials is a major problem faced by the process industry. It is important to ascertain whether such a system is safe or if it will undergo ignition for a particular set of conditions. In this paper, a three-component model of this system is considered which includes exothermic oxidation and endothermic evaporation processes. By assuming a slow rate of consumption of fuel and oxygen, the behaviour of the full system can be approximated and the safe and dangerous regions of parameter space can be identified. The effect of changes in parameters such as the size and the endothermicity are discussed in detail.

The effect of diffusion on the autoignition of combustible fluids in insulation materials

Ocean plankton populations as excitable media

In a recent paper we proposed a simple ODE model for the behaviour of populations of phytoplankton and zooplankton which had a mathematical structure analogous to models of excitable media. That model comprised a two-component system, in which limiting effects on the phytoplankton growth rate such as nutrient shortage and self-shading were represented parametrically. Here, we demonstrate the relationship of such a two-component system to a general class of three-component models in which nutrient is more realistically regarded as a third evolving variable, and self-shading is included as a growth rate modulation. We derive conditions for the existence and stability of equilibrium states which are generally valid for this class, and interprete the behaviour of particular models, proposed elsewhere, within this picture.

Equilibria, Stability and Excitability in a General Class of Plankton Population Models

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Papers

Spatial effects in the thermal runaway of combustible fluids in insulation materials

The effect of diffusion on the autoignition of combustible fluids in insulation materials

Ocean plankton populations as excitable media

Equilibria, Stability and Excitability in a General Class of Plankton Population Models