Properties of localized oscillatory excitation in a nonlinear oscillatory field

We analyzed the dynamics of a nonlinear oscillatory field composed of radial isochron clocks (RICs) or Stuart-Landau (SL) oscillators, which are the simplest dynamic systems that have one stable limit cycle around one unstable equilibrium. According to our computer simulation results, the nonlinear oscillatory field with two kinds of Mexican-hat-type connection had the function of several peak detections of the external input by localized oscillatory excitation areas. Moreover, the nonlinear oscillatory field could realize in-phase phase locking within each localized oscillatory excitation area, and could maximize the phase difference between the different localized oscillatory excitation areas. As the Amari (1977) model of the nerve field provided a mathematical base for the self-organizing map (SOM) algorithm, this nonlinear oscillatory field is expected to provide a theoretical base for the oscillatory SOM algorithm.