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What are some applications to the Van der Pol equation? Are there any physical examples?

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Can you explain a bit what this equation is in the question? From the answer you have got I see that it is interesting. But one should see from reading only the question, that the issue is legitimate and the closevotes it has are not justified... So please explain a bit more. –  Dilaton Jun 19 '13 at 18:46
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closed as not a real question by Brandon Enright, Chris White, Waffle's Crazy Peanut, David Z Jun 20 '13 at 2:04

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

1 Answer

Extracts from this ref

"Since its introduction in the 1920’s, the Van der Pol equation has been a prototype for systems with self-excited limit cycle oscillations. The classical experimental setup of the system is the oscillator with vacuum triode. The investigations of the forced Van der Pol oscillator behaviour have carried out by many researchers. The equation has been studied over wide parameter regimes, from perturbations of harmonic motion to relaxation oscillations. It was much attention dedicated to investigations of the peculiarities of the Van der Pol oscillator behaviour under external periodic (sinusoidal) force and, in particular, the synchronization phenomena and the dynamical chaos appearing . The Van der Pol equation is now concerned as a basic model for oscillatory processes in physics, electronics, biology, neurology, sociology and economics . Van der Pol himself built a number of electronic circuit models of the human heart to study the range of stability of heart dynamics. His investigations with adding an external driving signal were analogous to the situation in which a real heart is driven by a pacemaker. He was interested in finding out, using his entrainment work, how to stabilize a heart's irregular beating or "arrhythmias". Since then it has been used by scientists to model a variety of physical and biological phenomena. For instance, in biology, the van der Pol equation has been used as the basis of a model of coupled neurons in the gastric mill circuit of the stomatogastric ganglion . The Fitzhugh–Nagumo equation is a planar vector field that extends the van der Pol equation as a model for action potentials of neurons. In seismology, the van der Pol equation has been used in the development a model of the interaction of two plates in a geological fault" .

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Minor comment to the answer (v1): In the future please link to abstract pages rather than pdf files, e.g., arxiv.org/abs/0803.1658 –  Qmechanic Jun 19 '13 at 18:50
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