Cynthia Nixon and Governor Andrew Cuomo faced off on Wednesday night for 60 white knuckled minutes and the results did not disappoint! Well, maybe it was a little disappointing that so much time in the only debate of the Democratic gubernatorial primary was spent on the topics of bridge renaming and teaching children about the menace of marijuana. But the answers the candidates gave—on transportation, on healthcare, on corporate personhood and Shakespeare and helicopters—were somewhat illuminating! [ more › ] Gothamist https://ift.tt/2wuziXz August 31, 2018 at 01:42AM
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 ...
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