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This volume contains most of the talks presented at the Journ~es de la Soci~t~ Math~ma~ique de France entitled "Rhythms in Biology and other fields of application -Determi nistic and Stochastic Approaches" held in Luminy from the 14th th to the 18 of September 1981. The aim of our meeting was to bring together scien tists from different disciplines to discuss a common topic and to stimulate exchanges between participants. We hope that this goal was reached. This volume is divided into four chapters. In each one the papers are arranged in alphabetical order by first author. Chapters one and two contain papers devoted to descrip tion or modelling of rhythmic biolog.ical phenomena. Chapters three and four deal with models for the study of rhythms invol ving the use of deterministic or stochastic tools capable of fruitful transfer to Biology. We are pleased that these Proceedings appear in a series which constitutes an interface between Biologists and Mathema ticians. We are indebted to all who provided us with their help, particularly the Centre International de Rencontres Math~matiques (C.I.R.M.) at Luminy, the Soci~t~ Mathematique de France (S.M.F.), the Delegation aux Relations Universitaires Internationales (D.R.U.I.) and the Laboratoire d'Informatique et de Math~matiques Appliquees de Grenoble (I.M.A.G.). Special thanks are due to Mrs. A. Litman for her dedi cation and her efficiency throughout the organization of this meeting. G~enobie, Vecembe~ 1982.
Table des matières
1 Experiments and Modelling in Biology.- Simulation of the entrainment of the respiratory rhythm by two conceptually different models.- Glycolytic oscillations: an attempt to an "in vitro" reconstruction of the higher part of glycolysis: modelling and experimental approach.- Medical exploration of some rhythmic phenomena: a topological semeiology.- Spatio-temporal organization in immobilized enzyme systems.- Stereological analysis of circadian rhythms in nucleoli of rat sympathetic neurons.- Formalization of adrenal-postpituitory circadian rhythms by the model for the regulation of agonistic-antagonistic couples. Parameter identification.- 2 Theoretical Study of Biological Models.- The spruce budworm-forest and other ecosystems.- On the conservation of physiological function in a population of interactive and self replicative units.- Dynamics and stability of induction of the lactose operon of Escherischia Coli.- Automata networks as models for biological systems: a survey.- A critical discussion of plausible models for relay and oscillation of cyclic-AMP in Dictyostelium cells.- Fully asynchronous logical description of networks comprising feedback loops.- The rotor in reaction-diffusion problems and in sudden cardiac death.- 3 Deterministic Modelling of Rhythms.- Spatio-temporal oscillations of a cellular automaton in excitable media.- On the use of renormalization technics in the study of discrete population models in one dimension.- Hydrodynamics and cell division.- On the solutions of some differential equation in IR3 with small parameter.- Self-pulsing in ring-lasers.- Numerical analysis of the behaviour of an almost periodic solution to a periodic differential equation, an example of successive bifurcations of invariant tori.- 4 Stochastic Modelling ofRhythms.- Evolutive spectral analysis by autoregressive process of isotopic climatic data from Antartica.- Optimal randomness in foraging movement: a central place model.- A model for weather cycles based on daily rainfall occurrence.- A statistical approach to difference-delay equation modelling in ecology-two case studies.- Identification and modelling techniques for biological rhythms.- Chaotic curves.- Time series analysis and biology.- Large deviations and more or less rare events in population dynamics.
