Modeling of nonlinear dynamical systems based on deterministic learning and structural stability

Recently, a deterministic learning (DL) theory was proposed for accurate modeling or identification of the dynamics of nonlinear dynamical systems. In this paper, we further investigate the problem of modeling or identification of the partial derivative of dynamics for dynamical systems. Based on the locally accurate identification of the unknown system dynamics via deterministic learning, the modeling or identification of its partial derivative of dynamics along the periodic or periodic-like system trajectory is obtained by introducing the mathematical concept of directional derivative. With the accurate identification of the system dynamics and its partial derivative of dynamics, a C¹-norm modeling approach is then proposed from the perspective of structural stability. This will provide incentives for further applications in the classification for dynamical systems and patterns as well as the prediction of bifurcation and chaos. Simulation studies are included to demonstrate the effectiveness of this modeling approach.