Henon Attractor: Overview and Resources

The Henon attractor is a type of discrete-time dynamical system that exhibits chaotic behavior. It was introduced by French mathematician Michel Henon in 1976 as a simplified model of the Poincare section of the Lorenz model. The Henon map is widely studied in the field of chaos theory and nonlinear dynamics due to its simplicity and rich behavior.

Overview

The Henon Map

The Henon map is defined by a simple set of iterative equations:

where:

• and are the coordinates at the -th iteration,
• and are parameters that determine the behavior of the system.

Characteristics

The Henon map can produce a range of behaviors depending on the values of and . For the classic Henon attractor, the parameters are typically set to and . Under these conditions, the system exhibits chaotic behavior, and the iterated points create a fractal structure in the - plane. The Henon attractor is notable for its sensitivity to initial conditions, a hallmark of chaotic systems.

Visualization

The attractor is visualized by iterating the map many times and plotting the points . The resulting image reveals a complex, butterfly-shaped fractal pattern that never repeats.

Resources

Articles and Papers

• Wikipedia Entry: Henon Map
• Original Paper by Michel Henon: A Two-Dimensional Mapping with a Strange Attractor

Interactive Tools and Simulations

• Desmos Graphing Calculator: Henon Map
• Wolfram Demonstrations Project: Henon Attractor

Books

• "Chaos in Dynamical Systems" by Edward Ott: Amazon Link
• "Nonlinear Dynamics and Chaos" by Steven H. Strogatz: Amazon Link

Code and Implementation

• Python Implementation: Henon Map in Python
• MATLAB Implementation: MATLAB Code for Henon Map

The Henon attractor remains a fundamental example in the study of chaotic systems and nonlinear dynamics. The resources provided above will help you delve into the fascinating world of the Henon map and explore its chaotic behavior.