Linear stability analysis of systems with Preisach memory

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June 2009, 11(4): 997-1018. doi: 10.3934/dcdsb.2009.11.997

Linear stability analysis of systems with Preisach memory

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

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

Received June 2008 Revised December 2008 Published April 2009

Abstract
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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: local stability analysis, operator-differential equation, Preisach model., Periodic solution.

Mathematics Subject Classification: Primary: 47J40; Secondary: 34C2.

Citation: Alexander Pimenov, Dmitrii I. Rachinskii. Linear stability analysis of systems with Preisach memory. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 997-1018. doi: 10.3934/dcdsb.2009.11.997

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