A procedure for obtaining general nonlinear Fokker–Planck equations

Fernando D. Nobre, Evaldo M.F. Curado and G. Rowlands

Physica A: Statistical Mechanics and its Applications, 2004, vol. 334, issue 1, 109-118

Abstract: A procedure for deriving general nonlinear Fokker–Planck equations (FPEs) directly from the master equation is presented. The nonlinear effects are introduced in the transition probabilities, which present a dependence on the probabilities for finding the system in a given state. It is shown that the FPEs, obtained from master equations describing transitions among discrete and continuous sets of states, are identical. Within such a procedure, we construct nonlinear FPEs that appear to be very general. Our general FPEs recover, as particular cases, nonlinear FPEs investigated previously by many authors, introduced on a purely phenomenological basis, and they lead to the possibility of more complete and complex diffusive equations.

Keywords: Master equation; Nonlinear Fokker–Planck equation; Nonextensive thermostatistics (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:334:y:2004:i:1:p:109-118

DOI: 10.1016/j.physa.2003.11.023

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