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A new mathematical model of hysteresis, based upon the previous work of Chun and Stromsmoe, is introduced. The model not only provides for hysteresis loops at frequencies down to dc but allows for extensive control over higher frequency behavior. Loop widening with increased frequency can be included, as well as loop narrowing (a phenomenon present in the i-v curves of fluorescent lamps). Loop widening can be reduced to insignificant amounts beyond an upper threshold or can be eliminated all together. Other behavior with frequency variation can be provided once the model is understood. Applications of the model include the simulation of ferrite "memory" cells and the analysis of hysteretic systems capable of operating at arbitrarily low frequencies.