We have this vision of immigrants arriving by ship, seeing the Statue of Liberty and landing at Ellis Island to start their new American lives. But thousands of people never made it that far. Instead, they were detained at Swinburne and Hoffman Islands, two tiny islands in our harbor that were used as quarantine islands from the 1870s until the 1920s. [ more › ] Gothamist https://ift.tt/2TZrlDU November 28, 2018 at 12:00PM
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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