Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780429972195
Author: Steven H. Strogatz
Publisher: Taylor & Francis
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Chapter 10.4, Problem 8E
Interpretation Introduction

Interpretation:

To solve the Lorenz equation numerically for σ = 10, β = 83, and r near to 166.

  1. To show if r = 166 all trajectories are attracted to a stable limit cycle and plot both the xz projection of the cycle, and the time series x(t).

  2. To show that if r = 166.2 the trajectory looks like the old limit cycle for much of the time but occasionally it is interrupted by chaotic bursts.

  3. To show that as r increases the burst become more frequent and last longer.

Concept Introduction:

  • The three-different system of ordinary differential equations are,

    dx(t)dt = σ(y-x)dy(t)dt = x(r-z)-ydz(t)dt = xy-bz

    Here the variable x, y and z is the system at time t and σ, ρ, β are the positive parameter of the Lorenz equation.

  • The Lorenz system has able to reduce the system into three - dimension state space and determine the place of first chaotic system. And intermittency is the rate of a signal that rotates randomly between randomly, points and moderately shorts asymmetrical bursts.

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