Periodic solutions of a switching dynamical system in the plane

Abstract

The non linear differential equation is considered. We investigate the number of nontrivial periodic solutions of this equation depending on k ≥ 0 for µ < 0 fixed. The results obtained can be used in a problem of time optimal control for the Van der Pol equation in order to describe the process of control.

Keywords:

• Switching dynamical system
• periodic solutions
• limit cycle
• AMS(MOS): 34C25, 34C35, 70K10

This work was done while the second author held a C.N.R. Felloship and was visiting the University of Florence.The second author expresses her gratitude to professor R. Conti for his invitation and to the Institute of Mathematics “Ulisse Dini” for its hospitality.

This work was done while the second author held a C.N.R. Felloship and was visiting the University of Florence.The second author expresses her gratitude to professor R. Conti for his invitation and to the Institute of Mathematics “Ulisse Dini” for its hospitality.

Notes

This work was done while the second author held a C.N.R. Felloship and was visiting the University of Florence.The second author expresses her gratitude to professor R. Conti for his invitation and to the Institute of Mathematics “Ulisse Dini” for its hospitality.

Additional information

Notes on contributors

Gabriele Villari

Zhang Zhifen