What are van der Pol equation used for?

The Van der Pol equation is now concerned as a basic model for oscillatory processes in physics, electronics, biology, neurology, sociology and economics [17]. Van der Pol himself built a number of electronic circuit models of the human heart to study the range of stability of heart dynamics.

Is Van der Pol chaotic?

Forced Van der Pol oscillator Chaotic behaviour in the Van der Pol oscillator with sinusoidal forcing. The nonlinear damping parameter is equal to μ = 8.53, while the forcing has amplitude A = 1.2 and angular frequency ω = 2π / 10.

What is MU in van der Pol equation?

The parameter μ controls the amount of nonlinear damping. For any initial condition, the solution approach a periodic solution.

What does Van der Pol mean?

from the raised land
Van der Pol (also “Van de Pol”, “Van de Poll”, “Van den Pol” or “Van Pol”) is a Dutch, toponymic surname, originally meaning “from the raised land”.

What kind of oscillator is van der Pol?

Van der Pol oscillator. The van der Pol oscillator is an oscillator with nonlinear damping governed by the second-order differential equation where is the dynamical variable and a parameter. This model was proposed by Balthasar van der Pol (1889-1959) in 1920 when he was an engineer working for Philips Company (in the Netherlands).

When did Reona Esaki invent the van der Pol oscillator?

After Reona Esaki (1925-) invented the tunnel diode in 1957, making the van der Pol oscillator with electrical circuits became much simpler. Figure 5: An electrical circuit with a tunnel diode for the van der Pol oscillator.

How is the van der Pol equation used in science?

The Van der Pol equation has a long history of being used in both the physical and biological sciences. For instance, in biology, Fitzhugh and Nagumo extended the equation in a planar field as a model for action potentials of neurons.

Is the van der Pol system a Lienard system?

Therefore, the dynamics of the system is expected to be restricted in some area around the fixed point. Actually, the van der Pol system ( 1) satisfies the Liénard’s theorem ensuring that there is a stable limit cycle in the phase space .The van der Pol system is therefore a Liénard system .