xt+1 = 1.0 + μ (xt cosθt - yt sinθt)

yt+1 = μ (xt sinθt + yt cosθt)

θt = a - b/(1.0 + xt2  + yt2)

case 1

parameters: μ = 0.9, a = 0.4, b = 6.0

Lyapunov exponents (log with base-e): 0.50752, -0.71824
Lyapunov Dimension: 1.7066

The sum of the Lyapunov exponents  is theoretically the same as 2 ln(μ).

case 2

parameters: μ = 0.83, a = 0.4, b = 6.0

Lyapunov exponents (log with base-e): 0.39272, -0.76538
Lyapunov Dimension: 1.5131

The sum of the Lyapunov exponents  is theoretically the same as 2 ln(μ).

Reference

Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system

Kensuke Ikeda

Optics Communications, 30, 257–261 (1979)

DOI: 10.1016/0030-4018(79)90090-7

Computing the Lyapunov spectrum of a dynamical system from an observed time series

Reggie Brown, Paul Bryant, and Henry Don Isaac Abarbanel

Physical Review A 43, 2787-2806 (1991)

DOI: 10.1103/PhysRevA.43.2787

Chaos and Time-Series Analysis (p. 424)

Julien Clinton Sprott

Oxford University Press (2001/Sep/27)

ISBN-10: 0198508409

ISBN-13: 978-0198508403

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