def dP_dt(P, t, a=1.0, b=1.0, c=1.0, d=1.0):
    """
AKA Lotka-Volterra equations: pair of first order, non-linear ordinary
    differential equations representing a simplified model of the change in
    populations of two species which interact via predation.

dx/dt = x*(a - b*y); dy/dt = -y*(c -d*x)

a, b, c, d are parameters which are assumed to be positive.
    """
    return [P[0]*(a - b*P[1]), -P[1]*(c - d*P[0])]