] we proposed a method which extends this basin of attraction by use of systematized trial and error converging procedure. In order to do that, we combine a deterministic method with a Simulated Annealing algorithm to refine initial guesses for periodic orbit search. In other words, the goal of this stochastic method is to enable the determination of initial guesses with sufficient accuracy to lay them into the basin of attraction of a fast converging algorithm like the Newton-Raphson algorithm. As a consequence of the underlying stochastic nature of the algorithm, it enables one to determine several different periodic orbits for the considered dynamical system by launching the algorithm several times.