We address the biological dynamics problem of the persistence of several species in conditions of non-existence of an equilibrium, including an example of stabilization by predation and the very controversial “competitive exclusion”. We give normal forms for various examples of such persistence and comments on the involved topology, which implies the presence of exceptional heteroclinic connections binding equilibria on the boundary.

The present work is a contribution to the understanding of the sempiternal problem of the “burden of factor two” implied by sexual reproduction versus asexual one, as males are energy consumers not contributing to the production of offspring. We construct a deterministic mathematical model in population dynamics where a species enjoys both sexual and parthenogenetic capabilities of reproduction and lives on a limited resource. We then show how polygamy implies instability of a parthenogenetic population with a small number of sexually (...) born males. This instability implies evolution of the system towards an attractor involving both populations. We also exhibit the analogy with a parasite/host system. (shrink)

A la croisée des chemins de la vulgarisation, de l'histoire et de la philosophie des sciences, l'auteur explore la nature de la connaissance et de la recherche via un mode d'exposition faisant largement appel à l'analogie. [extrait de la 4è de couv.].