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Solving Van der Pol equation with ivp_solve

Van der Pol’s differential equation is The equation describes a system with nonlinear damping, the degree of damping given by μ. If μ = 0 the system is linear and undamped, but for positive μ the system is nonlinear and damped. We will plot the phase portrait for the solution to Van der Pol’s equation in Python using SciPy’s new ODE solver ivp_solve . The function ivp_solve does not solve second-order systems of equations directly. It solves systems of first-order equations, but a second-order differential equation can be recast as a pair of first-order equations by introducing the first derivative as a new variable. Since y is the derivative of x , the phase portrait is just the plot of ( x , y ). If μ = 0, we have a simple harmonic oscillator and the phase portrait is simply a circle. For larger values of μ the solutions enter limiting cycles, but the cycles are more complicated than just circles. Here’s the Python code that made the plot. from scipy import linspace from ...

Lawyer: 'Socialite Grifter' Anna Sorokin 'Had To Do It Her Way' (And Steal $275,000)

Opening statements were made in the "Socialite Grifter" trial on Wednesday, and both sides provided extremely different reasons why Anna Sorokin allegedly scammed a number of people and institutions out of $275,000. [ more › ] Gothamist https://ift.tt/2HXgI0E March 29, 2019 at 12:33AM

NYC's Deadliest Trash Hauling Company Is Going Out Of Business

Sanitation Salvage, the embattled private trash hauling company responsible for two deaths and countless safety violations , has surrendered its license and is going out of business. The company announced the decision in a letter sent to the Business Integrity Commission this week, city officials said. [ more › ] Gothamist https://ift.tt/2TYFVLx November 28, 2018 at 07:14PM

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