Understanding Hysteresis Curves: Mathematical Modeling for Nonlinear ODEs

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The discussion centers on the mathematical modeling of hysteresis curves, specifically the relationship between magnetic field strength (H) and magnetic flux density (B). A proposed nonlinear ordinary differential equation (ODE) is presented to describe the hysteresis cycle. However, it is noted that B(H) is not a single-valued function of H, complicating the mathematical deduction of the hysteresis curve. The conversation emphasizes the challenges in deriving a differential equation for B as a function of H due to its inherent nonlinearity. Overall, the complexities of modeling hysteresis in this context are highlighted.
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the idea is , if we have the magnetic field strength (H) and magnetic flux density (B) so we represent the 'hysteresis cycle' to be B(H)=B my question is could we deduce mathematically the hysteresis curve ?? for example if we can provide a model of a nonlinear ODE so

\frac{dB}{dH}= B^{r}- (1/B)

or something similar, i would be interested in the differential equation satisfied by B=B(H) thanks.
 
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Since B(H) is not a single valued function, or any simple function, of H, you cannot do what you are trying.
 
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