Five years ago, the city changed the way it handled animal abuse complaints, with the NYPD taking over enforcement duties from the ASPCA. Now, the police department and animal welfare organization are touting the success of their partnership, noting there have been nearly 700 arrests and the treatment of 3,300 victims of animal cruelty. [ more › ] Gothamist http://bit.ly/2FXy5y9 January 31, 2019 at 12:11AM
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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