Dynamical systems: A tool for analysis and design of silicon half center oscillators

In this paper, a new oscillator circuit for central pattern generator systems has been proposed. Switched-capacitor technique which enables controllable, more accurate and stable resistance has been used. Oscillation frequency can be easily controlled by the frequency of switching which is very useful for global change of oscillation frequency in an array of oscillators. SPICE simulation and dynamical systems analysis have shown that when used as a single oscillator, the proposed circuit is able to produce a phase response curve (PRC) close to the one of a lamprey central pattern generator (CPG) system. Applying averaging theory to the system of coupled oscillators, we obtain averaged H and G functions for unidirectional and bidirectional coupling cases. Analysis of these functions shows our circuit's superior capability to achieve fast entrained oscillation with sensory feedback and reach equilibrium even with high frequency mismatch.