Complex Systems Group is a multidisciplinary research group recognized officially by Universidad Politécnica de Madrid.

The group has extensive experience in the study of nonlinear dynamic systems, having developed mathematical and computer tools for the study and characterization of them.

Within the field of Hamiltonian systems, special attention has been devoted to chaotic molecular systems, studying the vibrational dynamics of triatomic molecules using models with two degrees of freedom, using the ideas of nonlinear dynamics to rationalize them. This study has been addressed by focusing on the chaotic behavior of these systems, both from the point of view of quantum mechanics as classical mechanics, in order to establish a comparison between the results of both. We have developed several techniques that allow characterization of regular or chaotic behavior of classical trajectories of the systems, among which are the Poincare Surface of Section Composite, computation of periodic orbits, Liapunov exponents, Local Frequency Analysis, Multifractal Analysis etc..

On the other hand, also has extensive experience in the study of dynamical systems by introducing the effects of memory, both short and long term. In particular, we have studied in detail the behavior of the Logistic map based on the memory capacity of the model. Also, in recent years we have worked hard at studying the effect of memory in cellular automata, achieving significant results in this field.