Some people treat their morning rush hour commute as a balletic dance, one in which they try their best not to infringe on other people's space despite the increasingly limited space available on any given train. Other people treat it as a winner-takes-all battlefield, kill or be killed, seat or be unseated. But usually, even when things get verbally heated between passengers, they don't turn into a prolonged stun gun stand-off. [ more › ] Gothamist https://ift.tt/2TYHMQM November 28, 2018 at 08:17PM
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 ...
Comments
Post a Comment