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Physical Review Letters
Volumn 69, Issue 5, 1992, Pages 761-764
Transition from chaotic to nonchaotic behavior in randomly driven systems
Author keywords

[No Author keywords available]
Indexed keywords

EID: 0000435791     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.69.761     Document Type: Article
Times cited : (89)
References (12)
  • 1
    • 84927381036 scopus 로고    scopus 로고
    • See, for example, G. L. Baker and J. P. Gollub, Chaotic Dynamics: An Introduction (Cambridge Univ. Press, Cambridge, 1990); also, Noise and Chaos in Nonlinear Dynamical Systems, edited by F. Moss, L. A. Lugiato, and W. Schleich (Cambridge Univ. Press, Cambridge, 1990).
  • 7
    • 84927381035 scopus 로고    scopus 로고
    • Usually in Monte Carlo simulations there is an ``accept-reject'' part of each step also (see Ref. [3]), to allow for inexact energy conservation in integrating the equations of motion. This does not alter our results, and we have removed it in the simulations shown here, having verified that our results are insensitive to the step length used in numerical integration.
  • 8
    • 84927381034 scopus 로고    scopus 로고
    • We have verified, using various subtractive and linear congruential pseudorandom number generators in choosing velocities, that our results do not depend on the details of the generator used.
  • 9
    • 0002121327 scopus 로고
    • There is no reason for the usual considerations limiting passage through energy barriers large compared to the temperature to be circumvented in the present problem [see, ]. Presumably, for particles started in different regions, separated by large potential barriers, the time for them to ``find'' each other must be at least as great as the typical barrier penetration time.
    • (1943) Rev. Mod. Phys. , vol.15 , pp. 1
    • Chandrasekar, S.1
  • 10
    • 84927381033 scopus 로고    scopus 로고
    • The argument breaks down because pairs of particles entering a region tend to align themselves to some extent along the most slowly contracting direction in that region. Thus, the naive formal extension of the one-dimensional result to higher dimensions gives only an upper bound on the contraction rate as τ -> 0 and does not rule out an average dilation.
  • 11
    • 84927381032 scopus 로고    scopus 로고
    • The only potential we investigated for which Eq. (1) did not give a reasonable estimate was the quartic-plus-quadratic potential V(x,y) = x2y2+ ( x2+ y2) / n for large values of n. As n -> inf, this potential becomes nonbounding along the x and y axes, and the observed contraction rate tends to zero.

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