An extension of the Jiles–Atherton (J–A) magnetic hysteresis model is proposed in the paper. The physical J–A model has been substituted with the specially chosen mathematical Chua model. The proposed model produces identical results to those of the original J–A model for the static magnetic hysteresis loop. The new model permits the inclusion of a wide variety of additional effects observed for ferromagnetic materials without invalidating the well-known and broadly used J–A model parameters. Thus, it is possible to effectively model phenomena, whose detailed physical model would require complex mathematical calculations.