  hysteresis is the dependence of the output of a system not only on its current input, but also on its history of past inputs. the dependence arises because the history affects the value of an internal state. to predict its future outputs, either its internal state or its history must be known. if a given input alternately increases and decreases, a typical mark of hysteresis is that the output forms a loop as in the figure. such loops may occur purely because of a dynamic lag between input and output. this effect disappears as the input changes more slowly. this effect meets the description of hysteresis given above, but is often referred to as rate-dependent hysteresis to distinguish it from hysteresis with a more durable memory effect. hysteresis occurs in ferromagnetic materials and ferroelectric materials, as well as in the deformation of some materials (such as rubber bands and shape-memory alloys) in response to a varying force. in natural systems hysteresis is often associated with irreversible thermodynamic change. many artificial systems are designed to have hysteresis: for example, in thermostats and schmitt triggers, hysteresis is used to avoid unwanted rapid switching. hysteresis has been identified in many other fields, including economics and biology.  ==etymology and history== the term "hysteresis" is derived from , an ancient greek word meaning "deficiency" or "lagging behind". it was coined around 1890 by sir james alfred ewing to describe the behaviour of magnetic materials. some early work on describing hysteresis in mechanical systems was performed by james clerk maxwell. subsequently, hysteretic models have received significant attention in the works of ferenc preisach (preisach model of hysteresis), louis nÃ©el and d. h. everett in connection with magnetism and absorption. a more formal mathematical theory of systems with hysteresis was developed in the 1970s by a group of russian mathematicians led by mark krasnosel'skii. he suggested an investigation of hysteresis phenomena using the theory of nonlinear operators.{{cite book|first=isaak d.|last= mayergoyz|title= mathematical models of hysteresis and their application
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