Abstract: Interactions among two or three different species can be modeled using nonlinear discrete maps based upon logistic map.
The considered interactions can be of mutual benefits (symbiosis), competition or predator-prey type. The strength of the interaction depends upon real coupling parameters. The study is done by considering classical tools of nonlinear discrete dynamical systems (singularities, stability, attractors, basin, bifurcations, critical manifolds...). The different kinds of interactions give rise to many various and complex phenomena, depending upon the strength of the coupling parameter. Multistability can be obtained with fractal basin boundaries, chaotic attractors can be observed. The evolution of the attractors and their basin under parameter variation can be explained using bifurcation analysis and critical manifold study.
Such studies can give rise to applications in Ecology, Biology or Economics.
All these works have been done in collaboration with R. Lopez-Ruiz, from University of Zaragoza, Spain.

Brief Biography of the Speaker:
Daniele Fournier-Prunaret obtained a Ph.D. under the supervision of Pr. C. Mira, eminent specialist of Nonlinear Dynamical Systems, then a Doctorat d'Etat at the University Paul Sabatier of Toulouse, France, respectively in 1981 and 1987. She is currently Professor at the National Institute of Applied Sciences (INSA) in Toulouse, France and the Head of the LATTIS (Toulouse Laboratory of Technology and System Engineering). Her research and teaching activities concern Modelisation and Analysis of Nonlinear Dynamical Systems, focusing more particularly on the study of Chaos and Applications to Telecommunications, Secure Transmissions and Biology. She is the author of around 100 papers in international journals and conferences related to the study of Nonlinear Maps.