# Jiles-Atherton model of hysteresis

In my quest for finding a good algorithm to draw hysteresis curve,I have found Jiles-Atherton model which seems to be a rather new model. But I have trouble understanding some of the variables/constants that are used in the formulation.There seems to be a rather similar question here. What I have trouble understanding is that what are Mirr and Man? And how is it possible that M is defined using Mirr and Man, and yet in the definition of Man we use M ?

I have updated my answer to the question you referenced; maybe the nature of the various components will now be clearer.

The model equations are indeed challenging. One can substitute for $M$ in the equation for $M_{an}$, leaving a pair of simultaneous equations, one transcendental (for $M_{an}$) and one differential (for $M_{irr}$).

$$M_{an} = M_s \left[\coth\left(\frac{H+ \alpha (cM_{an}+(1-c)M_{irr})}{A}- \frac{A}{H+\alpha (cM_{an}+(1-c)M_{irr})} \right) \right]$$

$$\frac{dM_{irr}}{dH} = \frac{M_{an} - M_{irr}}{k \delta - \alpha (M_{an}- M_{irr})}$$

After solving for $M_{an}$ and $M_{irr}$, $M=cM_{an}+(1-c)M_{irr}$ can be determined.

As far as I know, numerical methods are required.