Bernie Sanders Political Dynasty? Senator's Son, Stepdaughter Run For Office

Both the son and stepdaughter of Sen. Bernie Sanders, I-Vt., are running for office in 2018.

The son of the Vermont senator and 2016 presidential candidate is seeking a congressional seat in New Hampshire. Sanders' stepdaughter is running for mayor of Burlington, Vt., an office he once held.

(Image credit: Susan Walsh/AP)

News : NPR http://ift.tt/2GRCqPZ February 28, 2018 at 01:03AM

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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 ...

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