Computing Bifurcation Diagrams for Dynamical Systems
Calculation of bifurcation diagrams for dynamical systems, chaotic systems, and high-dimensional chaotic systems with algorithm implementation details
Simulation of a Chaotic System
MATLAB program for simulating chaotic systems. lyapunov.m serves as the main computational routine; qi_hyper.m provides an implementation example (Qi system) using qi_hyper_lyap.m to calculate all Lyapunov exponents and qi_hyper_lyapDim.m for fractal dimension computation. The program can be adapted for other systems with minor modifications. Verified to be more efficient and accurate than alternative Lyapunov exponent calculation methods.
Phase Diagram and Poincaré Section Plotting Tool for Chaotic Systems
This program generates phase diagrams and Poincaré sections for chaotic systems. Users simply need to define the corresponding chaotic differential equations to automatically visualize the system's dynamics. The implementation supports parameter customization and employs numerical integration methods for accurate trajectory computation.
Logistic Map and Strange Attractors Part 1: The Logistic Map
Logistic Map and Strange Attractors Part 1: Logistic Mapping - The Road to Chaos. While chaotic systems display complex behavior, their underlying dynamics (motion equations) aren't necessarily complicated. Simple systems with few parameters can exhibit chaotic phenomena too. Taking the one-dimensional population model as an example, where yn represents the current population count in a region, this model demonstrates how basic mathematical formulations can lead to chaotic behavior.
MATLAB Implementation for Plotting Chaotic Attractors in Chaotic Systems
A beginner-friendly MATLAB M-file program for visualizing chaotic attractors, developed during my initial exploration of chaos theory. This implementation provides practical code examples for researchers starting their journey in chaotic systems analysis.
Computing Lyapunov Exponents for Chaotic Systems
This method provides an efficient approach to calculate Lyapunov exponents for chaotic systems by modifying their dynamic equations, with implementation demonstrated through numerical algorithms and Jacobian matrix computations.
Calculation of Lyapunov Exponents
Computation of Lyapunov exponents applicable to all chaotic systems, with implementation approaches and algorithm considerations
Visualizing Chaos and Critical Chaos in the Duffing Chaotic System
Exploring chaotic and critical chaotic phenomena in the Duffing oscillator system through computational modeling and visualization techniques
Chaos Masking Encryption Method for Secure Chaotic Communication
Under univariate driving coupling synchronization between two chaotic systems, implementing chaos masking encryption to achieve secure chaotic communication, with code implementation focusing on synchronization algorithms and encryption masking techniques.
MATLAB Implementation of False Nearest Neighbors and Cao's Method for Determining Embedding Dimension in Chaotic Systems
MATLAB source code implementing false nearest neighbors method and Cao's method to calculate embedding dimension for chaotic systems. Ready-to-run code with detailed algorithm explanations and practical applications.