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...

activation and deactivation dynamics of a spiking neuron. In turn, the Van der Pol oscillator is a special case of the FitzHugh–Nagumo model, with a = b = 0 {\displaystyle...

{3}{8}}\,\varepsilon \,\right)\,t{\Bigr )}\right].\,} We solve the van der Pol oscillator only up to order 2. This method can be continued indefinitely in...

Balthasar van der Pol (1889–1959), Dutch physicist a.o. known for the Van der Pol oscillator and the Bonhoeffer-van der Pol model Jaap van der Poll (1914–2010)...

leading to a Hopf bifurcation and the appearance of limit cycles. The van der Pol oscillator is one such model that has been used extensively in the mathematical...

Balthasar van der Pol (27 January 1889 – 6 October 1959) was a Dutch physicist. Van der Pol began his studies of physics in Utrecht in 1911. J. A. Fleming...

mathematical model of a relaxation oscillator, the influential Van der Pol oscillator model, in 1920. Van der Pol borrowed the term relaxation from mechanics;...

all linear oscillators must have negative resistance. The first analysis of a nonlinear electronic oscillator model, the Van der Pol oscillator, was done...

notation. This system is often called the Van der Pol oscillator. Applying periodic averaging to this nonlinear oscillator provides qualitative knowledge of the...

is a fixed point. Damped harmonic motion, see animation (right). Van der Pol oscillator see picture (bottom right). A phase portrait represents the directional...

dx}+f(x)v+g(x)=0} which is an Abel equation of the second kind. The Van der Pol oscillator d 2 x d t 2 − μ ( 1 − x 2 ) d x d t + x = 0 {\displaystyle {d^{2}x...

about the dynamics of the system, such as the limit cycle of the Van der Pol oscillator shown in the diagram. Here the horizontal axis gives the position...

Society. 20 (3): 180–9. doi:10.1112/jlms/s1-20.3.180. See also: Van der Pol oscillator Smale, Stephen (January 1960). "Morse inequalities for a dynamical...

circuits exhibit limit cycle oscillations, which inspired the original Van der Pol model. The control of respiration and hematopoiesis, as appearing in...

Van der Pol oscillator is a non-conservative oscillator with non-linear damping. It was originally proposed by Dutch physicist Balthasar van der Pol while...

system are given by this last proposition. Consider the classical Van der Pol oscillator written with ordinary differential equations: { d x d t = μ ( 1...

Skarya Archived 2015-12-22 at the Wayback Machine Van der Pol Oscillator Equations Shaw-Pol chaotic oscillator Archived 2015-12-22 at the Wayback Machine The...

Phase portrait of a continuous-time dynamical system, the Van der Pol oscillator....

Stephen Smale while studying the behavior of the orbits of the van der Pol oscillator. The action of the map is defined geometrically by squishing the...

unsaturated water flow Self-balancing unicycle Sine-Gordon equation Van der Pol oscillator Vlasov equation Aleksandr Mikhailovich Lyapunov Dynamical system...

penthode and gyrator Bernard Tellegen and Balthasar van der Pol developer of Van der Pol oscillator, were TU Delft faculty. Currently Vic Hayes, and the...

asymptotic stability. Consider the following equation, based on the Van der Pol oscillator equation with the friction term changed: y ¨ + y − ε ( y ˙ 3 3 −...

and physics after a year. He worked with Balthasar van der Pol, known for the Van der Pol oscillator, and Frans Michel Penning, known for Penning ionization...

Lorenz system Lotka–Volterra equations Mackey–Glass equations Rabinovich–Fabrikant equations Rössler attractor Three-body problem Van der Pol oscillator...

Phase portrait of the Van der Pol oscillator, a one-dimensional system. Phase space was the original object of study in symplectic geometry....

began to collaborate studying the equations, in particular the Van der Pol oscillator, which greatly surprised the two: For something to do we went on...

Liénard system of equations, which are a generalization of the Van der Pol oscillator equation. The following process is also illustrated from rightside...

for x3 cbnd = initial(x1 <= 2.0); % Initial event constraint x1 Van der Pol Oscillator Minimize: J x , t = x 3 ( t f ) {\displaystyle {\begin{matrix}J_{x...

constructible polygons, twin primes, set theory, statistics, and the Van der Pol oscillator. As David Singmaster writes, many of these topics are the subject...

Phase portrait of the Van der Pol oscillator...