Oscillating dynamical system with nonlinear damping
In the study of dynamical systems, the van der Pol oscillator (named for Dutch physicist Balthasar van der Pol) is a non-conservative, oscillating system with non-linear damping. It evolves in time according to the second-order differential equation
where x is the position coordinate—which is a function of the time t—and μ is a scalar parameter indicating the nonlinearity and the strength of the damping.
van der Pol oscillator phase plot, with μ varying from 0.1 to 3.0. The green lines are the x-nullclines.The same oscillator phase plot, but with Liénard transform.The Van der Pol Oscillator simulated with the Brain Dynamics Toolbox[1]Evolution of the limit cycle in the phase plane. The limit cycle begins as a circle and, with varying μ, becomes increasingly sharp. An example of a relaxation oscillator.
^Heitmann, S., Breakspear, M (2017–2022) Brain Dynamics Toolbox. bdtoolbox.org doi.org/10.5281/zenodo.5625923
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