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Journal of Statistical Physics

, Volume 171, Issue 2, pp 361–381 | Cite as

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

  • Alexandr A. Barsuk
  • Florentin Paladi
Article
  • 410 Downloads

Abstract

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.

Keywords

Phase transitions Metastable state Bifurcation and stability analysis 

Notes

Acknowledgements

Authors gratefully acknowledge support provided by the Moldova State University through the Grant No. 15.817.02.29F, and the Academy of Sciences of Moldova through the STCU Project No. 6219. Authors are also indebted to anonymous referees for constructive comments and suggestions.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsMoldova State UniversityChișinăuRepublic of Moldova

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