Chapter 12.2, Problem 8E

Interpretation Introduction

Interpretation:

To explore numerically the implications of the changing of the parameter a of the Henon map by keeping the parameter b constant.

Concept Introduction:

• The Henon map is a two-dimensional map witha strange attractor. It captures the essential features of the Lorenz system but also has an adjustable amount ofdissipation.

• A map is the difference equation which follows ${\text{x}}_{\text{n+1}}{\text{= f(x}}_{\text{n}}\text{)}$.

• Computationally, maps are beneficial over differential equations as maps are faster to simulate, and their solutions can be followed more accurately for longer times.

• Periodic doubling is a type of a discrete dynamical system bifurcation in which even a minor change in the control parameter leads to double the period of the original system.

• An attractor is defined as the lowest unit at which the point cannot decompose into two or more attractors with distinct basins of attraction.