Dynamic reconstruction of chaotic systems from inter-spike intervals using least squares support vector machines

This work presents a methodology for dynamic reconstruction of chaotic systems from inter-spike interval (ISI) time series obtained via integrate-and-fire (IF) models. In this methodology, least squares support vector machines (LSSVMs) have been employed for approximating the dynamic behaviors of the systems under investigation. Higher generalization capability and avoidance of local minima constitute the main reasons behind the choice of LSSVMs as the approximation tool. Simulation results have shown that established LSSVM models possess great potential for the reconstruction of chaotic dynamics; in other words, they are able to estimate some dynamic invariants of the underlying chaotic systems as well as they can accurately predict short-term evolution within the horizon of predictability. Moreover, LSSVM models maintain their reconstruction performance even in the case of the existence of noisy data.