The pseudo-Hopf bifurcation for planar discontinuous piecewise linear differential systems

Arbitrary Number of Limit Cycles for Planar Discontinuous Piecewise Linear Differential Systems with Two Zones

For any given positive integer n we show the existence of a class of discontinuous piecewise linear differential systems with two zones in the plane having exactly n hyperbolic limit cycles. Moreover, all the points on the separation boundary between the two zones are of sewing type, except the origin which is the only equilibrium point.

Limit cycles of Discontinuous Piecewise Linear differential Systems

We study the bifurcation of limit cycles from the periodic orbits of a 2−dimensional (respectively 4−dimensional) linear center in R perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (respectively 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This uppe...

Planar Bimodal Piecewise Linear Systems

Generalized Hopf bifurcation for non-smooth planar dynamical systems

In this paper, we study the existence of periodic orbits bifurcating from stationary solutions in a non-smooth planar dynamical system. This phenomenon is interpreted as generalized Hopf bifurcation. In the case of smoothness, Hopf bifurcation is characterized by a pair of complex conjugate eigenvalues crossing through the pure imaginary axis. This method does not apply to a non-smooth system d...

Generalized Hopf bifurcation in a class of planar switched systems

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