Transition to nonchaotic behavior in a Brownian-type motion

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. {\bf 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.