1. Delay equations are of wide relevance to natural x=f(x1) [7], but the rapid oscillations make any dynamical systems, particularly in medicine and such easy comparison opaque. In this paper we focus physiology. For example, models of respiration [1 on the Mackey—Glass equation [2], which can be and cell maturation [2] naturally include significant written in the form (1), with delays; other s...

This paper proposes a Genetic Programming-Based Modeling (GPM) algorithm on chaotic time series. GP is used here to search for appropriate model structures in function space, and the Particle Swarm Optimization (PSO) algorithm is used for Nonlinear Parameter Estimation (NPE) of dynamic model structures. In addition, GPM integrates the results of Nonlinear Time Series Analysis (NTSA) to adjust t...

Neural networks are a popular representation for inducing single-step predictors for chaotic times series. For complex time series it is often the case that a large number of hidden units must be used to reliably acquire appropriate predictors. This paper describes an evolutionary method that evolves a class of dynamic systems with a form similar to neural networks but requiring fewer computati...

There are many systems that can be described as chaotic: The readings from seismic monitoring stations in mines which describe the rock dynamics, from EKG which describe the fibrillation of a cardiac patient’s heart, and the share prices in financial markets which describe the optimism about the earning potential of companies are examples of observations of deterministic, non−linear, dynamical ...

Chaotic maps can mimic random behavior in a quite impressive way. In particular, those possessing a generating partition can produce any symbolic sequence by properly choosing the initial state. We study in this letter the ability of chaotic maps to generate order patterns and come to the conclusion that their performance in this respect falls short of expectations. This result reveals some bas...

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the ...

This paper presents a new algorithm that combines perturbation theory and genetic programming for modeling and forecasting real-world chaotic time series. Both perturbation theory and time series modeling have to build symbolic models for very complex system dynamics. Perturbation theory does not work without well-defined system equation. Difficulties in modeling time series lie in the fact tha...

The accurate traffic flow time series prediction is the prerequisite for achieving traffic flow inducible system. Aiming at the issue about multi-step prediction traffic flow chaotic time series, the traffic flow Volterra Neural Network (VNN) rapid learning algorithm is proposed. Combing with the chaos theory and the Volterra functional analysis, method of the truncation order and the truncatio...