To plot the time delayed trajectory for the given function for various values of τ and to find whether the constructed attractor appear to be a torus. To find which τ seems optimal and construct trajectories in three dimensions. Concept Introduction: 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. A strange attractor is an attractor thatexhibits sensitive dependence on its initial conditions. Strangeattractors areoften fractal sets. The torus is a surface which is formed by rotating a closed loop in a circle which lies in the same plane without intersecting.

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Chapter 12.4, Problem 2E

Interpretation Introduction

Interpretation:

To plot the time delayed trajectory for the given function for various values of τ and to find whether the constructed attractor appear to be a torus.

To find which τ seems optimal and construct trajectories in three dimensions.

Concept Introduction:

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.

A strange attractor is an attractor thatexhibits sensitive dependence on its initial conditions. Strangeattractors areoften fractal sets.

The torus is a surface which is formed by rotating a closed loop in a circle which lies in the same plane without intersecting.

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