At 68, Aisha is a native New Yorker figuring out her exit strategy. In 2014, she moved to a rent-stabilized apartment in Brooklyn's Sheepshead Bay neighborhood. She pays $1,485 a month for a one-bedroom on a librarian’s salary. But Aisha, who asked that we withhold her last name to avoid problems with her landlord, figures it’s only a matter of time before her rent goes up beyond what she can afford. “It’s just not economically feasible,” she said, about staying in the city long-term. “I can live here but I can’t travel or do anything more than pay rent and just survive.” Even her financial adviser agreed, telling her, "Pray that you don’t get sick." [ more › ] Gothamist https://ift.tt/2TG3EPh March 28, 2019 at 11:00PM
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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