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Evolution of the system with multiplicative noise

Author

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  • Olemskoi, Alexander I.
  • Kharchenko, Dmitrii O.

Abstract

The governed equations for the order parameter, one- and two-time correlators are obtained for systems with white multiplicative noise. We consider the noise whose amplitude depends on stochastic variable as xa where 012, when the system is disordered, the correlator behaves in the course of time non-monotonically, whereas the autocorrelator increases monotonically. At a<12 the phase portrait of the system divides into two domains: at small initial values of the order parameter, the system evolves to a disordered state, as above; within the ordered domain it is attracted to the point with finite values of the autocorrelator and order parameter. The long-time asymptotes are defined to show that, within the disordered domain, the autocorrelator decays hyperbolically and the order parameter behaves as a power-law function with fractional exponent −2(1−a). Correspondingly, within the ordered domain, the behaviour of both dependencies is exponential with an index proportional to −tlnt.

Suggested Citation

  • Olemskoi, Alexander I. & Kharchenko, Dmitrii O., 2001. "Evolution of the system with multiplicative noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 178-188.
    • Handle: RePEc:eee:phsmap:v:293:y:2001:i:1:p:178-188
    DOI: 10.1016/S0378-4371(00)00601-4
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