Differentiability of evolution operators for dynamical systems with hysteresis

A Pokrovskii, T Power, D Rachinskii, A Zhezherun
2006 Journal of Physics, Conference Series  
Differentiability of evolution operators for dynamical systems with hysteresis To cite this article: A Pokrovskii et al 2006 J. Phys.: Conf. Ser. 55 171 View the article online for updates and enhancements. Related content On the integration of an ODE involving the derivative of a Preisach nonlinearity D Flynn and O Rasskazov -On transport in dynamical systems L V Polterovich -Stochastic aspects of hysteresis I D Mayergoyz and M Dimian -Recent citations Memory and adaptive behavior in
more » ... dynamics: anti-predator behavior as a case study Alexander Pimenov et al -Robust homoclinic orbits in planar systems with Preisach hysteresis operator Alexander Pimenov and Dmitrii Rachinskii -Hopf Bifurcation in Symmetric Networks of Coupled Oscillators with Hysteresis Z. Balanov et al -This content was downloaded from IP address on 26/07 Abstract. Hysteresis is a collective name for strongly nonlinear phenomena which occur in engineering, physical and economic systems. The wording 'strongly nonlinear' means that linearization cannot encapsulate the observed effects. In particular, standard linearization techniques are not applicable in the analysis of dynamical systems with hysteresis nonlinearities. Nevertheless, evolution operators of such dynamical systems typically have derivatives at many "important" points, which is enough to develop efficient modifications of gradient methods, linear stability analysis methods, etc. In this paper, we suggest a linearization algorithm for dynamical systems with the Preisach hysteresis operator. We present and justify an algorithm for calculation of the derivative of the Poincare map for scalar equations with a periodic solution of a simple form. We also suggest a version of this algorithm for a general class of non-periodic solutions of multi-dimensional equations with the Preisach nonlinearity.
doi:10.1088/1742-6596/55/1/017 fatcat:uvikomvdinb47kgfs4dgoaiyvq