Limit cycles of discontinuous piecewise differential systems formed by linear centers in R2 and separated by two circles

Bifurcation of Limit Cycles from a Focus-Parabolic-Type Critical Point in Piecewise Smooth Cubic Systems

“…where H 5 is given by (12). Under condition a 4 ̸ = 0, we obtain condition (F 8 ) under which V 10 ̸ = 0.…”

“…where H 2 is given by (12). Consequently, when (F 2 ) is satisfied, V 2 = • • • = V 9 = 0 and V 10 ̸ = 0, implying that (0, 0) is a weak focus of order 9 of system ( 2).…”

“…where H 3 is given by (12). If H 3 ̸ = 0, then (0, 0) is a weak focus of order 9 of system (2) when the condition (F 5 ) is satisfied.…”

“…where H 6 is given by (12). When V 10 ̸ = 0 and under condition (F 9 ), (0, 0) is a weak focus of order 9 of system (2).…”

“…In [11], Zou and Küpper investigated generalized Hopf bifurcations and further considered the existence of periodic orbits bifurcating from a corner in a PWS planar dynamical system. The number of limit cycles for a class of planar PWS systems formed by the center and separated by two circles was investigated by Anacleto et al in [12]. Furthermore, in [13], Zhang and Du studied the number of limit cycles of planar PWS systems bifurcated from the center and weak focus.…”