Nonlinear Fokker-Planck Equations - Fundamentals and Applications
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Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions.
It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution).
The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions.
Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.
"The author discusses the theory and application of nonlinear Fokker-Planck equations to the description of the nonlinear dynamics of many-body systems ... . The principles and concepts of the theory are carefully exposited, along with simple examples and a very large list of references, illustrating the wide applicability to natural phenomena occurring in fields as diverse as physics, mathematics, biology, neurophysics, psychology, social sciences and population dynamics. The book will be very useful for researchers and graduate students interested or working in these areas." (Vitor R. Vieira, Mathematical Reviews, Issue 2006 h)
"The book focuses on common fundamental physical mechanisms present in diverse research fields. ... The book may be a resource of mathematical problems in a field with diverse applications: each chapter gives an outline of examples and applications of various partial differential equations and an approach towards equilibrium of their solutions (H-theorems). A concept of negative stochastic feedback, with biological motivations, may be found interesting." (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1071, 2005)