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1
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85037244976
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While there has been no formal definitions of low-dimensional versus high-dimensional chaos, here we take the notion that low-dimensional chaos is characterized by one positive Lyapunov exponent, and high-dimensional chaos by more than one
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While there has been no formal definitions of low-dimensional versus high-dimensional chaos, here we take the notion that low-dimensional chaos is characterized by one positive Lyapunov exponent, and high-dimensional chaos by more than one.
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14
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85037223679
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The necessary ingredient for the transition here is that the driver is deeply in a chaotic state, regardless of its own route to chaos
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The necessary ingredient for the transition here is that the driver is deeply in a chaotic state, regardless of its own route to chaos.
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15
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44049111231
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See, for example, F. J. Romeiras, Physica D 58, 165 (1992)
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(1992)
Physica D
, vol.58
, pp. 165
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Romeiras, F.J.1
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25
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85037183372
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High-dimensional chaos with more than two positive Lyapunov exponents can be studied in a similar manner
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High-dimensional chaos with more than two positive Lyapunov exponents can be studied in a similar manner.
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27
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44949272537
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L. YuPhysica D 53, 102 (1991).
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(1991)
Physica D
, vol.53
, pp. 102
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Yu, L.1
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31
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85037194624
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For a continuous-time flow, one of the Lyapunov exponents, the one along the flow, must be zero. Thus, in Fig. 33, at the transition to high-dimensional chaos, (Formula presented) changes from zero to being positive and (Formula presented) changes from being negative to zero, but the negative part of (Formula presented) before the transition and the positive part of (Formula presented) after the transition appear to be continuous through the transition
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For a continuous-time flow, one of the Lyapunov exponents, the one along the flow, must be zero. Thus, in Fig. 33, at the transition to high-dimensional chaos, (Formula presented) changes from zero to being positive and (Formula presented) changes from being negative to zero, but the negative part of (Formula presented) before the transition and the positive part of (Formula presented) after the transition appear to be continuous through the transition.
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