Universal scaling of Lyapunov exponents in coupled chaotic oscillators

Liu, Zonghua; Lai, Ying-Cheng; Matías, Manuel A.
Physical Review E 67, 045203 (R) (1-4) (2003)

We have uncovered a phenomenon in coupled chaotic oscillators where a subset
of Lyapunov exponents, which are originally zero in the absence of coupling,
can become positive as the coupling
is increased. This occurs for chaotic attractors having multiple scrolls,
such as the Lorenz attractor. We argue that the phenomenon is due to
the disturbance to the relative frequencies with which a trajectory visits
different scrolls of the attractor.
An algebraic scaling law is obtained which relates the Lyapunov exponents
with the coupling strength. The scaling law appears to be universal.

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