Adaptive Evaluation of Complex Dynamical Systems Using Low-Dimensional Neural Architectures

New methodology of adaptive monitoring and evaluation of complicated dynamic data is introduced. The major objectives are monitoring and evaluation of both instantaneous and long-term attributes of complex dynamic behavior, such as of chaotic systems and real-world dynamical systems. In the sense of monitoring, the methodology introduces a novel approach to quantification and visualization of cognitively observed system behavior in a real time without further processing of these observations. In the sense of evaluation, the methodology opens new possibilities for consequent qualitative and quantitative processing of cognitively monitored system behavior. Techniques and enhancements are introduced to improve the stability of low-dimensional neural architectures and to improve their capability in approximating nonlinear dynamical systems that behave complex in high-dimensional state space. Low-dimensional dynamic quadratic neural units enhanced as forced dynamic oscillators are introduced to improve the approximation quality of higher dimensional systems. However, the introduced methodology can be universally used for adaptive evaluation of dynamic behavior variability also with other neural architectures and adaptive models, and it can be used for theoretical chaotic systems as well as for real-word dynamical systems. Simulation results on applications to deterministic, however, highly chaotic time series are shown to explain the new methodology and to demonstrate its capability in sensitive and instantaneous detections of changing behavior, and these detections serve for monitoring and evaluating the level of determinism (predictability) in complex signals. Results of this new methodology are shown also for real-world data, and its limitations are discussed.