The Devil is in the details: Spectrum and eigenvalue distribution of the discrete Preisach memory model

Autor: Dmitrii Rachinskii, Tamás Kalmár-Nagy, Daniel Kim, Andreas Amann
Rok vydání: 2019
Předmět:
Zdroj: Communications in Nonlinear Science and Numerical Simulation. 77:1-17
ISSN: 1007-5704
Popis: We consider the adjacency matrix associated with a graph that describes transitions between the states of the discrete Preisach memory model. This matrix can also be associated with the “last-in-first-out” inventory management rule. We present an explicit solution for the spectrum by showing that the characteristic polynomial is the product of Chebyshev polynomials. The eigenvalue distribution (density of states) is explicitly calculated and is shown to approach a scaled Devil’s staircase. The eigenvectors of the adjacency matrix are also expressed analytically.
Databáze: OpenAIRE