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A non-conservative, oscillating system with non-linear damping, named after Dutch physicist Balthasar van der Pol. Learn about its history, forms, results, bifurcations, Hamiltonian and quantum versions.
Aug 15, 2024 · Learn about the van der Pol equation, a differential equation that describes self-sustaining oscillations in circuits with vacuum tubes. Find its derivation, properties, applications, and references.
Learn about the Van der Pol equation, a nonlinear second order differential equation with self-sustaining oscillations. See how it is derived from the Rayleigh equation, how it can be expressed as a system of differential equations, and how to visualize its solutions.
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Learn about the van der Pol equation, a second-order non-linear autonomous equation that models a vacuum tube or a spring-mass system with negative damping. Find out its properties, such as a unique non-zero periodic solution and a limit cycle, and see its applications and proofs.
May 13, 2022 · A non-linear second-order differential equation that describes auto-oscillations of a simple oscillating system. Learn about its history, solutions, asymptotic methods, and applications to external disturbances.
Jan 4, 2021 · This lecture uses the mutiple-timescale method to study the behavior of the van der Pol oscillator, a canonical equation of mathematical physics which highlights the rich and interesting...
- 16 min
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- Nathan Kutz
Learn about the van der Pol equation, a nonlinear oscillator modeled by a semiconductor device in an RLC circuit. Explore the equilibrium, stability, and phase portrait of the system.
