Systèmes dynamiques

The point or area at which something divides into two branches or parts: the point at which bifurcating occurs.

In dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden“qualitative” or topological change in its behaviour. Generally, at a bifurcation, the local stability properties of equilibria, periodic orbits, or other invariant sets changes

This lesson is a pedagogical synthesis designed for Master 1 students.
It begins with the principles of modeling via differential equations, then
develops three important biological applications: epidemic models, predator–
prey interactions, and competition between species. The emphasis is
on assumptions, derivation of models, equilibrium analysis, qualitative
interpretation, and mathematical reasoning.