Nonlinear dynamics of habituating systems: learning to ignore

Habituation – a phenomenon in which a dynamical system exhibits a diminishing response to successive stimulations that eventually recovers when the stimulus is withheld – is universally observed in living systems spanning from animals to single cells. Despite its prevalence, generic mechanisms for this fundamental form of learning remain poorly understood. Drawing inspiration from prior research on systems that respond adaptively to step inputs, we study habituation from a nonlinear dynamics perspective. This approach enables us to formalize classical hallmarks of habituation that have been experimentally identified in diverse organisms and stimulus scenarios. We use this framework to investigate distinct biochemical circuits capable of habituation. In particular, we introduce an extensible family of nonlinear modules that can hierarchically implement various hallmarks.