The systematic study of nonlinear systems with hysteresis has started in the last quarter of the twentieth century and it led to the appearance of the first monograph on this theme in 1983 . Since then, the interest in the identification, analysis and applications of hysteresis phenomena in diverse physical and social systems has been continuously growing [2-6] and it has extended far beyond the classical areas of magnetism and plasticity. For example, optical hysteresis , superconducting hysteresis  and economic hysteresis  became well-established scientific domains, and many pioneering studies appeared in other areas, such as ecology, biology, psychology, computer science, and wireless communications. A general overview of the state of the art in the area of hysteretic systems has been recently presented in the three-volume handbook Science of Hysteresis, edited by Mayergoyz and Bertotti .
Relation between noise and hysteresis has a long and sinuous history, from the Barkhausen work in the beginning of the last century to the current challenges in magnetic recording due to the superparamagnetic effect. While there are extensive studies dealing with various manifestations of noise in hysteretic phenomena, a systematic analysis of hysteretic materials and devices driven by noisy input has been rather limited. An important reason for this situation is related to the lack of general analytical tools for addressing complex non-Markovian processes found at the output of hysteretic systems. As opposed to memoryless linear and nonlinear systems, analyzing non-Markovian processes involves ad hoc techniques that are rarely suitable for studying another class of stochastic processes with memory. Our analytical approach to the analysis of noise passage through hysteretic systems is suitable for any Preisach systems by decomposing the general stochastic characteristics of the output into a superposition of characteristics for binary non-Markovian processes which can be embedded into multidimensional Markovian processes defined on graphs [9-11]. Another important limitation in this area of research is related to the fact that noise is usually an internal feature of a physical system with limited control from experimental point of view. Our experimental approach circumvents this difficulty by using electronic noise generators Hameg 8131-2, which provide a wide selection for noise characteristics, and a set of parallel-connected Schmidt triggers, which play the role of hysteretic rectangular loop operators . In addition, we developed a general numerical approach to complex hysteretic systems with stochastic inputs, which leads to a unitary framework for the analysis of various stochastic aspects of hysteresis, including thermal relaxation, data collapse, field cooling/zero field cooling, and noise passage . Various differential, integral, and algebraic models of hysteresis are considered while the input processes are generated from arbitrary given spectra. The resulting statistical technique, based on Monte-Carlo simulations, has been successfully tested against several analytical results available in the literature and has been implemented in the new version of HysterSoft by Dr. Petru Andrei . The developed method is suitable for the analysis of a wide range of noise induced phenomena in nonlinear systems with hysteresis from various areas of science and engineering, as well as for the design and control of diverse magnetic, micro-electromechanical, electronics and photonic devices with hysteresis. A special attention of this work has been devoted to noise influence on current magnetic recording techniques, as well as on several unconventional alternatives, such as spin polarized current assisted recording, precessional switching, toggle switching where temperature-dependent operating regions were obtained.
 M. A. Krasnoselskii and A. Pokrovskii, Systems with Hysteresis, Nauka, 1983 (English, 1989)
 I. D. Mayergoyz, Mathematical Models of Hysteresis, Springer (1991)
 A. Visintin, Differential Models of Hysteresis, Springer (1994)
 M. Brokate and J. Sprekels, Hysteresis and Phase Transitions, Springer (1996)
 N. N. Rosanov, Spatial Hysteresis and Optical Patterns, Springer (2002)
 I. D. Mayergoyz, Mathematical Models of Hysteresis and their Applications, Elsevier, (2003)
 J. B. Davids (ed), The Handbook of Economics Methodology, Edward Elgor (1998)
 I. D. Mayergoyz and G. Bertotti (eds.), Science of Hysteresis, Academic Press (2006)
 M. Dimian and I. Mayergoyz, Phys. Rev. E 70, 046124 (2004)
 M. Dimian, NANO 3 (5), 391–397 (2008)
 M. Dimian, E. Coca, and V. Popa, J. App. Phys. 105 (7), 07D515, (2009)
 M. Dimian, A. Gîndulescu, and P. Andrei, IEEE Trans. Magn. 46 (2), 266-269 (2010)
 HysterSoft ver. User Guide v. 1.8. Available: http://www.eng.fsu.edu/ms/HysterSoft