On the number of limit cycles in piecewise linear Liénard systems

Arnaud Tonnelier (1)

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In a previous paper [Tonnelier, 2002] we conjectured that a Liénard system of the form ẋ = p(x) - y, ẏ = 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

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-00000583v1⟩