Two continuous-time systems are used as case study for the aPBC--the forced van der Pol oscillator and Rossler system.
Forced van der Pol Oscillator. The forced van der Pol (vdP) oscillator is described by the nonlinear state space model (28):
On the other hand, it can be seen that for [epsilon] = 0.1 the motion of the Van Der Pol oscillator
is very nearly harmonic, exhibiting alternate compression and rarefaction of the density with a relatively small period [PHI] of about 6.3 [micro]s.
Wang, "Analog study of bifurcation structures in a Van der Pol oscillator
with a nonlinear restoring force," Physical Review E, vol.
The Van der Pol oscillator
is a self-maintained electrical circuit made up of an Inductor (L), a capacitor initially charged with a capacitance (C) and a non-linear resistance (R); all of them connected in series as indicated in Fig.
Consider the Van der Pol Oscillator
problem [6, 50]
They include recurrence quantification analysis of bipolar disorder performed using a Van der Pol oscillator
model, detecting low-dimensional chaos in small noisy sample sets, Alan Turing meets the Sphinx, fractal geometry in computer graphics and in virtual reality, buyer decisions in the US housing industry, secular variation in the climatic memory of five Italian deep lakes, and in everyday action notes for a mindscape of bioethics.
As a simple example, PLR can qualitatively analyze the behavior of an undriven van der Pol oscillator
, a simple nonlinear circuit consisting of a capacitor, an inductor, and a nonlinear resistor connected in series.
They found small traveling waves through the system support that lock the phase difference among all metronomes and they model the connections in terms of a Van der Pol oscillator
. Aragones and Guasch  presented a theoretical analysis of path propagation in a set of systems with similar structures.
Rimbu, "Bifurcation phenomena of the delay correlated noise driven Van der Pol oscillator
," General Physics, vol.
Venkatasubramanian, "Singularity induced bifurcation and the van der Pol oscillator
," IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.
Chen, "Asymptotic analytical solutions of the two-degree-of-freedom strongly nonlinear van der Pol oscillators
with cubic couple terms using extended homotopy analysis method," Acta Mechanica, vol.