Seminar: Chaos in Ecology

Chaos in Ecology:
Real Experiments, Implications, and Analytical Proofs

Speaker: Alfonso Ruiz, Bolay Institute of University of Szeged (Hungary)

Abstract: The purpose of this talk is to understand some practical effects of chaos in population dynamics. The main implication of erratic fluctuations typical of a chaotic system is that the long-time predictions are not possible. Besides this property, other important feature is that it is possible to reproduce, within the system and varying the initial conditions, all the possible outcomes of a coin-tossing experiment. Although the notion of chaos is now well understood from a theoretical point of view, it is hard to find evidence of chaotic behaviours in ecology. The main reason of this fact is the difficulty in manupulating and experimenting with ecological systems. A remarkable exception is the work in \cite{Cushing} where the authors derived a structured population model to study the growth of laboratory experiments of flour beetles Tribolium and their experiments confirmed the chaotic behaviour predicted by the model. To the best of my knowledge, this is the first time that the presence of chaos is detected in ecology from experimental data. However, there are no analytic proofs of these facts. An aim here will be to develop different strategies for proving analytically the existence of complex behaviours in different frameworks: discrete systems, ODE's, PDE's, or Delay differential equations. With our methodology, we confirm the experimental results in \cite{Cushing} and detect the presence of chaos in other classical models presented by May, Hastings, Guckenheimer or the classical Lotka-Volterra system. This talk is based on some joint papers with E. Liz, P.J. Torres, and F. Zanolin.