Good morning to everyone except the MTA, which seems to have decided that it's not going to work today and neither should you. The morning rush was marred by delays piling up on the 7, A/C/E, and B/D/F/M lines, and not all of the problems were formally announced and acknowledged on the MTA website. Meanwhile, planned work is here to derail your day before it even starts. [ more › ] Gothamist https://ift.tt/2AF3YGy November 29, 2018 at 07:30PM
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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