Nonlinear Fokker-Planck Equations

Fundamentals and Applications

  • Till Daniel Frank

Part of the Springer Series in Synergetics book series (SSSYN)

Table of contents

About this book

Introduction

Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, population dynamics, and computational physics.

Keywords

Complexity Fokker-Planck equation Nonextensive Thermodynamics Nonlinear Dynamcis Stochastic Processes entropy phase Transition thermodynamics

Authors and affiliations

  • Till Daniel Frank
    • 1
  1. 1.Institut für Theoretische PhysikUniversität MünsterMünsterGermany

Bibliographic information

  • DOI https://doi.org/10.1007/b137680
  • Copyright Information Springer-Verlag Berlin Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-21264-5
  • Online ISBN 978-3-540-26477-4
  • Series Print ISSN 0172-7389
  • About this book