On the number of limit cycles in piecewise linear Liénard systems

Arnaud Tonnelier (1)

1 CORTEX - Neuromimetic intelligence

In a previous paper [Tonnelier, 2002] we conjectured that a Liénard system of the form x' = p(x) − y, y' = x where p is piecewise linear on n + 1 intervals has up to 2n limit cycles. We construct here a general class of functions p satisfying this conjecture. Limit cycles are obtained from the bifurcation of the linear center.

Mots clés: Limit cycles; piecewise linear systems; Liénard systems

Domaines: Systèmes dynamiques [math.DS]

Arnaud Tonnelier. On the number of limit cycles in piecewise linear Liénard systems. International journal of bifurcation and chaos in applied sciences and engineering , 2005, 15 (4), pp.1417-1422. ⟨inria-00000583v2⟩