Hysteresis is the dependence of a system not only on its current environment but also on its past environment. This dependence arises due to the system can be in more than one internal state. To predict its future development, either its internal state or its history must be known.
If a given input alternately increases & decreases, the output tends to form a loop as in the figure. Though, loops may also occur because of a dynamic lag among input and output. Often, this effect is also referred to as hysteresis, or rate-dependent hysteresis.
In natural systems hysteresis is often associated with irreversible thermodynamic change. Many artificial systems are designed to have hysteresis: for instance, in thermostats and Schmitt triggers, hysteresis is formed by positive feedback to avoid unwanted rapid switching. Hysteresis has been identified in many other fields, with economics and biology.