Basins of Attraction and Perturbed Numerical Solutions using Euler’s Method

Any physical system corresponding to a two-dimensional vector field has some uncertainty in the true flow at any given point; this uncertainty may even vary in time. Analytic study of a dynamical system often shows that a given point is in the basin of attraction of an asymptotically stable fixed point, but uncertainty in the vector field may change the fixed point to which a trajectory is attracted. In many applications of dynamical systems, it is important to understand the impact of unexpect variations in the vector field. This paper investigates a particular two-dimensional vector field with numerical methods by perturbing the solution at each iteration of Euler’s method. We take the perturbation to be uniformly distributed in some interval [−k, k], and study the impact of varying the parameter k on the basins of attraction.