Stochastic Optimization for Detecting Periodic Orbits of Nonlinear Mappings

The detection of periodic orbits bears signi cance for the study of nonlinear mappings, since they can reveal crucial information on their dynamics. Recently, population based stochastic optimization algorithms were introduced to address problems where traditional gradient based approaches failed. The e ciency of these approaches in applications, triggered further research towards the development of more e cient variants. This work presents the principal concepts of applying concurrent stochastic population based approaches for the detection of periodic orbits, and also reports new results attained by the application of Memetic Algorithms on well known chaotic maps for periodic orbits with high period.