On the existence of hysteresis in a transition to chaos after a single bifurcation

C. Tresser , P. Coullet , A. Arneodo

We study and classify discontinuous transitions to chaotic behaviour occurring after a single bifurcation in real endomorphisms. This classification which can be extended to more realistic dynamical systems, relies on the possible existence of the hysteresis mechanism. We discuss the intermittency phenomenon as an evidence for transitions without hysteresis.

Mots clés: catastrophe theory; stochastic processes; turbulence; hysteresis; bifurcation; discontinuous transitions; chaotic behaviour; endomorphisms; dynamical systems; intermittency phenomenon

Domaines: Articles anciens

C. Tresser, P. Coullet, A. Arneodo. On the existence of hysteresis in a transition to chaos after a single bifurcation. Journal de Physique Lettres, 1980, 41 (10), pp.243-246. ⟨10.1051/jphyslet:019800041010024300⟩. ⟨jpa-00231770⟩