A method for finding stable-unstable bifurcation points of nonlinear dynamical systems by using a Particle Swarm Optimization algorithm

In this paper, we propose a method for finding stable-unstable bifurcation points of nonlinear dynamical systems by using a Particle Swarm Optimization (PSO) algorithm. Since the structure of systems can change suddenly at such points, it is desired to find them in advance for the purpose of engineering such as design, control, etc. We formulate a mathematical optimization problem to find a particular type of bifurcation points of nonlinear black-box systems, and we solve it numerically by employing a Particle Swarm Optimization (PSO) algorithm. Practicality of the proposed method is investigated by numerical experiments.