Linear stability analysis of systems with Preisach memory

Alexander Pimenov; Dmitrii I. Rachinskii

doi:10.3934/dcdsb.2009.11.997

Article Contents

2009, Volume 11, Issue 4: 997-1018. Doi: 10.3934/dcdsb.2009.11.997

This issue Previous Article Point-vortex interaction in an oscillatory deformation field: Hamiltonian dynamics, harmonic resonance and transition to chaos Next Article Pseudospectral method using generalized Laguerre functions for singular problems on unbounded domains

Linear stability analysis of systems with Preisach memory

Alexander Pimenov^1, and
Dmitrii I. Rachinskii^2,

1.
Department of Applied Mathematics, University College Cork
2.
Department of Applied Mathematics, University College Cork, Cork

Received: May 31, 2008

Revised: November 30, 2008

Published: October 2009

Abstract Related Papers Cited by

Abstract

We consider differential equations coupled with the input-output memory relation defined by the Preisach operator. The differential equation relates an instant value of the rate of change of the output of the Preisach operator with an instant value of its input. We propose an algorithm for the linearisation of the evolution operator of the system and apply it to define the characteristic multiplier of periodic solutions, which determines their stability. Examples of the system considered include models of terrestrial hydrology and electronic oscillators with hysteresis.

Keywords:

Mathematics Subject Classification: Primary: 47J40; Secondary: 34C25.

Citation:

Article Metrics

HTML views() PDF downloads(167) Cited by(0)

Linear stability analysis of systems with Preisach memory

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Linear stability analysis of systems with Preisach memory

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content