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 ...
New York home health aides who have been fighting to get paid for every hour they spend on the job had their hopes dashed Tuesday when the highest court in the state ruled that it’s legal for them to get paid for 13 hours of a 24-hour shift while caring for elderly and disabled people in their homes. [ more › ] Gothamist https://ift.tt/2FE4siZ March 28, 2019 at 09:37PM
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