A solvable molecular switch model for stable temporal information processing

This paper studies an input-driven one-state state-space model initially developed for an experimentally demonstrated dynamic molecular switch that switches like synapses in the brain do. The linear-in-the-state and nonlinear-in-the-input model is exactly solvable, and it is shown that it also possesses mathematical properties of convergence and fading memory that enable stable processing of time-varying inputs by nonlinear dynamical systems. Thus, the model exhibits the co-existence of biologically-inspired behavior and desirable mathematical properties for stable learning on sequential data. The results provide the basis for further study of DMSs as computation nodes in a network of interconnected DMSs that could potentially perform computational tasks that are out of the reach of a single DMS alone. They could also inspire more general exactly solvable models that can be fitted to emulate arbitrary physical devices that mimic brain-inspired behaviour and can perform stable computation on input signals.