Visualizations of Random Attractors Found Using Lyapunov Exponents
5 hours ago
- #dynamical systems
- #chaos theory
- #Lyapunov exponents
- Random attractors are found using Lyapunov exponents.
- A two-dimensional non-linear system, specifically the quadratic map, is used to represent chaotic systems.
- The Lyapunov exponent measures the average rate of divergence or convergence in a system, indicating chaos if positive.
- The largest Lyapunov exponent is typically considered to determine system behavior.
- Positive Lyapunov exponents indicate chaotic and unstable systems, negative exponents indicate stable systems, and zero indicates neutral stability.
- To create chaotic attractors, parameters in the quadratic equation are chosen randomly, and the system is iterated to compute the Lyapunov exponent.
- Different behaviors of the series include convergence to a fixed point, divergence to infinity, periodic orbits, or chaotic attractors.
- The software used to generate these images is highly selective, with most random parameter sets resulting in infinite series.
- References include key texts on chaos theory and dynamical systems.