Transition to nonchaotic behavior in a Brownian-type motion

B. Kaulakys; G. Vektaris

doi:10.1103/PhysRevE.52.2091

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Transition to nonchaotic behavior in a Brownian-type motion

B. Kaulakys and G. Vektaris

Institute of Theoretical Physics and Astronomy, A. Goštauto 12, 2600 Vilnius, Lithuania

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Phys. Rev. E 52, 2091 – Published 1 August, 1995

DOI: https://doi.org/10.1103/PhysRevE.52.2091

Abstract

A theoretical and numerical analysis of the transition from chaotic to nonchaotic behavior in an ensemble of particles with different initial conditions which move according to Newton’s equations in a bounding potential and are driven by an identical sequence of random forces [see S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992)] is presented. The threshold values of the parameters for transition from chaotic to nonchaotic behavior are defined on the basis of the map for distances between the particles and differences of velocity. Numerical analysis is fulfilled for one-dimensional Duffing V(x)= $x^{4}$ - $x^{2}$ and V(x)= $x^{4}$ potentials.

References (9)

S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992).
D. W. Heermann, Computer Simulation Methods in Theoretical Physics (Springer, Berlin, 1990).
In [1] the mixing $v^{new}$ =α $v^{old}$ + β $v^{ran}$ has been introduced. However, one can without loss of generality set β=1 together with replacement of temperature T by (1- $α^{2}$ )T.
A. Maritan and J. R. Banavar, Phys. Rev. Lett. 72, 1451 (1994).
D. Park, Classical Dynamics and Its Quantum Analogues (Springer, Berlin, 1990).
L. E. Reichl, The Transition to Chaos: In Conservative Classical Systems: Quantum Manifestations (Springer, Berlin, 1992).
A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).
J. D. Meiss, Rev. Mod. Phys. 64, 795 (1992).
J. M. Ottino et al., Science 257, 754 (1992).

[c1] S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992).

[c2] D. W. Heermann, Computer Simulation Methods in Theoretical Physics (Springer, Berlin, 1990).

[c3] In [1] the mixing $v^{new}$ =α $v^{old}$ + β $v^{ran}$ has been introduced. However, one can without loss of generality set β=1 together with replacement of temperature T by (1- $α^{2}$ )T.

[c4] A. Maritan and J. R. Banavar, Phys. Rev. Lett. 72, 1451 (1994).

[c5] D. Park, Classical Dynamics and Its Quantum Analogues (Springer, Berlin, 1990).

[c6] L. E. Reichl, The Transition to Chaos: In Conservative Classical Systems: Quantum Manifestations (Springer, Berlin, 1992).

[c7] A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983).

[c8] J. D. Meiss, Rev. Mod. Phys. 64, 795 (1992).

[c9] J. M. Ottino et al., Science 257, 754 (1992).

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Transition to nonchaotic behavior in a Brownian-type motion

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