Transition from strange nonchaotic to strange chaotic attractors

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 53, Issue 1, 1996, Pages 57-65

  Lai, Ying Cheng ^a  

^a UNIVERSITY OF KANSAS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003145080     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.57     Document Type: Article

References (26)

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13. The quasiperiodically forced pendulum has two nontrivial Lyapunov exponents LAMBDA and Λ prime that satisfy Λ prime = - ( p + Λ ), where p is the damping rate in Eq. (10). This can be seen by noting that Eq. (10) is actually a time-dependent flow of the form d φ / d t = v and d v / d t = - p ( v - cos φ ) + f (t). Taking the divergence of this flow, we obtain ( partial / partial v ) ( d v / d t ) + ( partial / partial φ ) ( d φ / d t ) = - p. Since this divergence is also the sum of the Lyapunov exponents, Eq. (13) holds. For large values of p, both LAMBDA and Λ prime are negative. The exponent Λ prime can be viewed as the exponential rate at which orbits in the three-dimensional phase space ( φ , v , z ) are attracted to the torus. For large p the rate is large, rendering the torus stable and difficult to destroy. As p decreases, - Λ prime becomes smaller. For p
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