Chapter 12.4, Problem 2E

Interpretation Introduction

Interpretation:

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

To find which $\text{τ}$ seems optimal and construct trajectories in three dimensions.

Concept Introduction:

• 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.

• 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.