Dynamic hysteresis in an autocatalytic reaction network

Abstract

Here we show that an autocatalytic reaction network can exhibit dynamic hysteresis as a result of the competition between its intrinsic relaxation time scale and that of the periodic drive. The autocatalytic reaction steps generate bistability in the concentration of the autocatalytic species, and periodic pumping of the product species provides the external drive. Hysteresis arises from the lag between the concentration response of the autocatalytic species and the external periodic drive. The resulting hysteresis-loop area quantifies the extent of the system's hysteretic response. Using the periodically driven Schl\"ogl model as a representative bistable chemical system, we use this loop area to determine how the magnitude of the hysteretic response is controlled by the driving protocol, intrinsic fluctuations, and the size of the system. Varying the driving frequency and the strength of the fluctuations causes a turnover of the hysteresis loop area, whereas the area changes monotonically with driving amplitude and system size. These trends identify the driving protocol and fluctuation strength as primary controls on the magnitude of dynamic hysteresis. In contrast to stochastic resonance, which is typically associated with weak periodic forcing and noise-assisted amplification, dynamic hysteresis can characterize the reaction-system response over a wider range of external control conditions. We further show that the delayed concentration response is mirrored in Shannon entropy and in the total entropy production rate, connecting dynamic hysteresis to information-theoretic and stochastic-thermodynamic measures of irreversibility. Overall, we identify and interpret the role of the controlling factors in chemical dynamic hysteresis and suggest implications for efficient chemical logic gates and eventually, chemical computers.