**Author details**

16 Nonlinearity, Bifurcation and Chaos - Theory and Applications

The flip bifurcations have been detected in the following (*ks* − *N*) plane: Subspace I when

Before the flip bifurcation the converter has a stable fixed point or T-periodic orbit. After the flip bifurcation the T-periodic orbit is unstable and the converter has a stable 2T-periodic orbit. Successive flip bifurcations and border-collision bifurcations are presented until the chaos formation. More details can be found in [2], [4], [15]. An illustrative example is shown

This bifurcation is associated with the appearance of a positive real characteristic multiplier in the unit cycle boundary (*mi* = 1). Figure 9 (*b*) shows the evolution of characteristic multipliers

The fold bifurcations have been detected in the following (*ks* − *N*) planes: Subspaces II and

Before the fold bifurcation the converter has two fixed points: one stable and other unstable. The stable fixed point is near to reference value. After the fold bifurcation the converter has not fixed points and the output is saturated. An illustrative case is presented in figure 10 (*b*).

This bifurcation is associated with the appearance of two conjugate complex characteristic multipliers in the unit cycle boundary. Figure 9 (*c*) shows the evolution of characteristic

The Neimark-Sacker bifurcations have been detected in the following (*ks* − *N*) planes: Subspace III for *τ* = 0 and Subspace I and III for *τ* > 0. The control subspaces with

Before the Neimark-Sacker bifurcation the converter has a stable fixed point or T-periodic orbit. After the Neimark-Sacker bifurcation the converter has quasi-periodic behavior and 2D-torus birth. The bifurcation diagram and the characteristic multipliers in the

*τ* = 0. The flip zone in the plane *τ* = 0 is presented in figure 8 (*b*).

when *N* is varied in a negative range for several *ks* and *τ* values.

**5.3. Neimark-Sacker bifurcations in** (*ks*, *N*, *τ*) **space**

Neimark-Sacker bifurcations are presented in figure 8 (*d*).

*5.3.2. Characteristics near to Neimark-Sacker bifurcation*

Neimark-Sacker transition are shown in figure 10 (*c*).

multipliers when *N* and *ks* are varied in positive ranges for *τ* > 1.

*5.1.1. Control subspaces*

in figure 10 (*a*).

*5.2.1. Control subspaces*

IV for (see figure 8 (*c*)).

*5.3.1. Control subspaces*

*5.1.2. Characteristics near to flip bifurcation*

**5.2. Fold bifurcations in** (*ks*, *N*, *τ*) **space**

*5.2.2. Characteristics near to fold bifurcation*

John Alexander Taborda

*Universidad del Magdalena - Facultad de Ingeniería - Programa de Ingeniería Electrónica - Magma Ingeniería - Santa Marta D.T.C.H., 2121630, Colombia*
