Sergei Petrovskii

TL;DR: The 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.

TL;DR: Current knowledge of transient dynamics is reviewed, showing that hitherto idiosyncratic and individual patterns can be classified into a coherent framework, with important general lessons and directions for future study.

TL;DR: Biological applications of reaction-diffusion waves is reviewed, which includes qualitative properties of travelling waves for the scalar reaction-Diffusion equation and for system of equations, complex nonlinear dynamics, numerous applications in physics, chemistry, biology, medicine.

TL;DR: Introduction Ecological Patterns in Time and Space Local structures Spatial and spatiotemporal structures An Overview of Modeling Approaches Models of temporal dynamics Classical One Population Models Isolated populations models Migration models A glance at discrete models A peek into chaos Interacting Populations A two-species predator-prey population model The classical Lotka-Volterra model Other types of ecosystems Global stability A food web More about chaos

TL;DR: It is shown that, when the local kinetics of the system is oscillatory, for a wide class of initial conditions the evolution of theSystem leads to the formation of a non-stationary irregular pattern corresponding to spatio-temporal chaos.