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The European Physical Journal Special Topics

, Volume 222, Issue 7, pp 1675–1684 | Cite as

Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field

  • G. Radons
  • A. Zienert
Regular Article

Abstract

Complex hysteresis is a well-known phenomenon in many branches of science. The most prominent examples come from materials with a complex microscopic structure such as magnetic materials, shape-memory alloys, or, porous materials. Their hysteretic behavior is characterized by the existence of multiple internal system states for a given external parameter and by a non-local memory. The input-output behavior of such systems is well studied and in a standard phenomenological approach described by the so-called Preisach operator. What is not well understood, are situations, where such a hysteretic system is dynamically coupled to its environment. Since the hysteretic sub-system provides a complicated form of nonlinearity, one expects non-trivial, possibly chaotic behavior of the combined dynamical system. We study such a combined dynamical system with hysteretic nonlinearity. In this original contribution a simple differential-operator equation with hysteretic damping, which describes a magnetic pendulum is considered. We find, for instance, a fractal dependence of the asymptotic behavior as function of the starting values. The sensitivity of the system to perturbations is investigated by several methods, such as the 0–1 test for chaos and sub-Lyapunov exponents. The power spectral density is also calculated and compared with analytical results for simple input-output scenarios.

Keywords

Radon Lyapunov Exponent European Physical Journal Special Topic Chaotic Behavior Energy Harvest 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Institute of Physics, Complex Systems and Nonlinear Dynamics, Chemnitz University of TechnologyChemnitzGermany
  2. 2.Institute for MechatronicsChemnitzGermany
  3. 3.Center for Microtechnologies, Chemnitz University of TechnologyChemnitzGermany

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