Abstract This paper proposes a technique to identify nonlinear dynamical systems with time delay. The sparse optimization algorithm is extended proposed combines cross-validation techniques from machine learning for automatic model selection and an algebraic operation preprocessing signals filter the noise removing dependence on initial conditions. We further integrate bootstrapping resampling ...

Almost all of the technical methods, which are used in the theory of nonlinear dynamical systems, originated in the theory of one dimensional dynamical systems. In this talk, a relation between nonlinear ergodic theorems, which are developed by Prof. Takahashi and other researchers, and the asymptotic behavior of one dimensional dynamical systems will be delivered, and moreover, application of ...

Dynamical systems attract much attention due to their wide applications. Many significant results have been obtained in this field from various points of view. The present paper is devoted to an algebraic method of integration of three-dimensional nonlinear time dependent dynamical systems admitting nonlinear superposition with four-dimensional Vessiot-Guldberg-Lie algebras L4. The invariance o...