Nonlinear Models of Interactions Among Two or Three
Species : Symbiosis, Prey-Predator, Competition
Professor Daniele Fournier-Prunaret
Director of LATTIS
Interactions among two or three different species can be
modeled using nonlinear discrete maps based upon
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.