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 x n+1 = f(x n ) . 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.

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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 xn+1= f(xn).

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.

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