From Independent to Coupled Hysterons: The Preisach Principle

Key ideas

• Step one, the classical model: a hysteretic output built from independent relays with a fixed density.
• Step two, van Hecke's extension: each relay's thresholds depend on the states of the others, through a coupling matrix that can be signed and asymmetric.
• Step three, the Preisach principle: the density itself becomes shaped by coupling, rather than a fixed constant.
• Includes the classical model and known interacting models as special cases, and works through a six-hysteron example of two coupled triads.

What it means for you

It gives Preisach a precise benchmark: your profile is measured against the same threshold-and-coupling form, so it is consistent rather than a mood reading.