One Step Forward: Periodic Computation in Dynamical Systems

The nonlinear dynamics of chaotic circuits generate a rich spectrum of signals. This observation suggests that these circuits could potentially provide an implementation of a novel framework of computation. In support of this hypothesis, computational complexity of the nervous system is achieved in large part through the nonlinear elements of electrically excitable membranes. In this study, we characterize the structure of the integral periodic components of signals generated by the chaotic inductor-diode (LD) circuit using a novel periodic decomposition. Specifically, we show that simple sinusoidal inputs, when passed through the LD circuit, can be used to store discrete, multiplexed periodic information. Further research could reveal principles of a periodic form of computation that can be implemented on simple dynamical systems with qualitatively complex behaviors. It is our hope that insights into the biological organizing principles of the nervous system will emerge from a precise, computational understanding of complex nonlinear systems such as the LD circuit.