Limit cycles for discontinuous quadratic differential systems with two zones

作者：Llibre Jaume; Mereu Ana C^*

来源：Journal of Mathematical Analysis and Applications, 2014, 413(2): 763-775.

DOI：10.1016/j.jmaa.2013.11.031

• Limit cycles
• Discontinuous quadratic systems
• Averaging theory
• Isochronous center

In this paper we study the maximum number of limit cycles given by the averaging theory of first order for discontinuous differential systems, which can bifurcate from the periodic orbits of the quadratic isochronous centers (x) over dot = -y + x(2), (y) over dot = x + xy and (x) over dot = -y + x(2) - y(2), (y) over dot = x + 2xy when they are perturbed inside the class of all discontinuous quadratic polynomial differential systems with the straight line of discontinuity y = 0. Comparing the obtained results for the discontinuous with the results for the continuous quadratic polynomial differential systems, this work shows that the discontinuous systems have at least 3 more limit cycles surrounding the origin than the continuous ones.

• 出版日期2014-5-15