Governor Andrew Cuomo made congestion pricing a centerpiece of his budget presentation earlier this month, pledging to raise $15 billion for transit improvements by tolling vehicles crossing bridges into Manhattan or traveling below 60th Street in Manhattan. According to a recent poll, 52 percent of New York State residents support congestion pricing, and that number climbs even higher for those living in the city. Missing from the conversation: Mayor Bill de Blasio, who at first said he did not "believe" in congestion pricing, and now says that the idea to toll cars coming into his city has nothing to do with him. [ more › ] Gothamist http://bit.ly/2Tm8G4f January 29, 2019 at 11:23PM
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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