97 Learning Markov-Chaev Embedded Recurrence Relations for Chaotic Time Series Analysis

This work explores Markov-chain structured recurrence relations for generation and perception of chaotic time series. A recurrence relation realized by a multi-layer neural network of radial basis functions (RBF) is employed to characterize the memory-less conditional expectation of a high order Markov process in short time scale. On the basis, a stochastic Markov chain is employed to emulate model switching among multiple recurrence relations embedded within chaotic time series. The high-order recurrence relation is expressed by a nonlinear RBF network derived by Levenberg-Marquardt learning subject to paired data auto-regressively sampling from dynamically segmented chaotic time series. The proposed Markov modeling is applied to synthesize chaotic time series of laser data. Numerical simulations show encouraging results.