Limit cycles in piecewise smooth differential systems of focus-focus and saddle-saddle dynamics

Document Type : Research Paper

Authors

1 Fergusson College (Autonomous)‎, ‎Pune‎, ‎India.

2 Abasaheb Garware College, Pune, India.

3 Department of Mathematics, Savitribai Phule Pune University, Pune, India.

Abstract

In this paper, we obtained the Poincare return maps for the planar piecewise linear differential systems of the type focus-focus. Normal forms for planar piecewise smooth systems with two zones of the type focus-focus and saddle-saddle, separated by a straight line and with a center at the origin, are obtained. Upper bounds for the number of limit cycles bifurcated from the period annulus of these normal forms due to perturbation by polynomial functions of any degree are established.

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Articles in Press, Accepted Manuscript
Available Online from 14 June 2024
  • Receive Date: 08 December 2023
  • Revise Date: 01 May 2024
  • Accept Date: 08 June 2024