Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2009-10-09
Nonlinear Sciences
Exactly Solvable and Integrable Systems
6 pages, 6 figures
Scientific paper
The equation of the Van der Pol oscillator, being characterized by a dissipative term, is non-Lagrangian. Appending an additional degree of freedom we bring the equation in the frame of action principle and thus introduce a one-way coupled system. As with the Van der Pol oscillator, the coupled system also involves only one parameter that controls the dynamics. The response system is described by a linear differential equation coupled nonlinearly to the drive system. In the linear approximation the equations of our coupled system coincide with those of the Bateman dual system (a pair of damped and anti-damped harmonic oscillators). The critical point of damped and anti-damped oscillators are stable and unstable for all physical values of the frictional coefficient $\mu$. Contrarily, the critical points of the drive- (Van der Pol) and response systems depend crucially on the values of $\mu$. These points are unstable for $\mu > 0$ while the critical point of the drive system is stable and that of the response system is unstable for $\mu < 0$. The one-way coupled system exhibits bifurcations which are different from those of the uncoupled Van der Pol oscillator. Our system is chaotic and we observe phase synchronization in the regime of dynamic chaos only for small values of $\mu$.
Das Uma
Ghosh Sangeeta
Talukdar Benoy
No associations
LandOfFree
One-way coupled Van der Pol system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with One-way coupled Van der Pol system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and One-way coupled Van der Pol system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-51161