Biological factors underlying regularity and chaos in aquatic ecosystems: Simple models of complex dynamics

Abstract

This work is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that reaction-diffusion mathematical models are an appropriate tool for searching and understanding basic mechanisms of complex spatio-temporal plankton dynamics and fractal properties ofplanktivorous fish school walks

Wave of Chaos: New Mechanism of Pattern Formation in Spatio-temporal Population Dynamics

“…2 and 3 corresponds to a chaotic dynamics. The strong sensitivity of the solutions of system (5) (6) to a small variation of the initial conditions in the parameter range corresponding to the formation of irregular non-stationary patterns is shown in Medvinsky et al (2000); the corresponding value of the dominant Lyapunov exponent is estimated as * D $0.001>0. Further on, accounting for these results, we will refer to the``smooth'' and``sharp'' patterns as regular and chaotic ones.…”

“…It was stated in Section 3 that the regime of irregular spatio-temporal oscillations arising in the prey predator model (5) (6) can be classified as chaos. That conclusion was made based on the results of the consideration of time series of the species densities (specifically, the power spectra), see , and on the analysis of the sensitivity of the solutions to small perturbations (Medvinsky et al, 2000). However, both approaches account for the spatial properties of the species distribution only in an implicit way.…”

Patchiness in a minimal nutrient — phytoplankton model

“…In particular, pattern formation due to the effects of diffusion and/or advection has been widely investigated, constituting a fascinating fi eld in modern natural sciences. For example, plankton patchiness has been among the central issues in mathematical modelling of aquatic ecosystems (Abraham 1998;Petrovskii and Malchow 1999;Medvinsky et al 2001Medvinsky et al , 2002.…”

Waves analysis and spatiotemporal pattern formation of an ecosystem model

“…In aquatic environments, such gradients occur because of the spatial distribution of the nutrients [7,8]. Horizontal diffusivities of phytoplankton (prey) and zooplankton (predator) are a well-studied example, and spatial inhomogeneities, in the distribution of the population can have an important impact on the dynamics of the ecosystem [1,9,5,[10][11][12]6]. In [10], Le Quéré et al developed a strategy for model evaluation, based on simulation of both past and presented mean states and variabilities, and identified potential sources of validation data for each.…”