# What are van der Pol equation used for?

## 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 .