Common Methods for Chaotic Time Series Analysis and Prediction

This document introduces fundamental methods for chaotic time series analysis and prediction. The implemented techniques include: - Chaotic time series generation methods utilizing mathematical mappings: * Logistic Map - ChaosAttractorsMain_Logistic.m employs the recursive equation xₙ₊₁ = rxₙ(1-xₙ) to demonstrate period-doubling bifurcations * Henon Map - ChaosAttractorsMain_Henon.m computes the system xₙ₊₁ = 1 - axₙ² + yₙ, yₙ₊₁ = bxₙ - Attractor modeling implementations for classical chaotic systems: * Lorenz Attractor - ChaosAttractorsMain_Lorenz.m solves the differential equation system using numerical integration (e.g., Runge-Kutta methods) * Duffing Attractor - ChaosAttractorsMain_Duffing.m simulates the nonlinear oscillator ẍ + δẋ + αx + βx³ = γcos(ωt) * Duffing2 Attractor - ChaosAttractorsMain_Duffing2.m implements modified Duffing oscillator configurations * Rossler Attractor - ChaosAttractorsMain_Rossler.m models simpler chaotic flow with three coupled nonlinear equations * Chens Attractor - ChaosAttractorsMain_Chens.m represents a multi-scroll chaotic system variant These methods cover core technologies in chaotic time series analysis, providing robust foundations for research and prediction applications. The toolbox will undergo continuous updates to enhance functionality and practical utility. Thank you for your interest!