Route to chaos in a circuit modeled by a 1-dimensional piecewise linear map

Danièle Fournier-Prunaret (1) , Pascal Charge (2)

1 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
2 IETR - Institut d'Électronique et des Technologies du numéRique

A very simple hybrid circuit proposed as chaos generator is studied. It is modeled using a 3-slopes piecewise linear map defined on [0,1] and depending upon three parameters. The parameter space is investigated in order to classify regions of existence of stable periodic orbits and regions associated with chaotic behaviors. Bifurcation curves are obtained numerically and analytically. Border collision bifurcations and homoclinic bifurcations occurring in cyclical chaotic regions leading to chaos in one-piece are detected.

Mots clés: piecewise linear bimodal map; chaos generator; border collision bifurcation

Domaines: Sciences de l'ingénieur [physics]

Danièle Fournier-Prunaret, Pascal Charge. Route to chaos in a circuit modeled by a 1-dimensional piecewise linear map. Nonlinear Theory and Its Applications, IEICE, 2012, 3 (4), pp.521-532. ⟨10.1587/nolta.3.521⟩. ⟨hal-00707750⟩