Dhystérésis

Dhystérésis, often referred to as hysteresis, is a phenomenon in which the state of a system depends on its history of inputs, not solely on the current stimulus. In a hysteretic system, the response to a given input can differ depending on the path taken to reach that input, producing a memory effect and typically a looped or lagging behavior when inputs are cycled.

Hysteresis occurs in a wide range of contexts. In magnetism, B-H curves show how magnetic flux depends on the history of magnetic field strength, with residual magnetization and coercivity. In mechanics and materials, viscoelastic damping and friction exhibit rate-dependent or rate-independent hysteresis. Electronic devices such as Schmitt triggers and certain memory elements (memristors) rely on hysteretic behavior. Thermal systems can display thermal hysteresis during phase transitions, while in biology and ecology, systems may shift between states only after crossing historical thresholds, creating persistence or regime shifts.

The defining features are memory and energy loss. The system’s response to changing input traces a loop in the input–output plane, and the area of this loop often corresponds to dissipated energy during a cycle. Thresholds or internal states separate branches of the response, leading to history-dependent behavior even under identical instantaneous inputs.

Modeling approaches include the Preisach model, which represents a complex hysteresis operator as a superposition of simpler elementary hysteresis operators, and the Prandtl–Ishlinskii model. These frameworks capture path dependence and are used in engineering, physics, and materials science to analyze and design systems with hysteretic behavior.