The Nonlinear Dynamic Conversion of Analog Signals into Excitation Patterns.pdfVIP

The Nonlinear Dynamic Conversion of Analog Signals into Excitation Patterns Gerold Baier and Markus Müller Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, 62210 Cuernavaca, Morelos, Mexico e-mail: baier@servm.fc.uaem.mx Abstract Local periodic perturbations induce frequency-dependent propagation waves in an excitable spatio-temporally chaotic system. We show how segments of noise-contaminated and chaotic perturbations induce characteristic sequences of excitations in the model system. Using a set of “tuned” excitable systems, it is possible to characterize signals by their spectral composition of excitation pattern. As an example we analyze an epileptic “spike-and-wave” time series. PACS numbers: 05.45.Gg; 05.45.Tp; 05.45Xt 1 For systems of diffusively coupled nonlinear oscillators it was found that excitable spatio-temporal chaos may undergo a generic pattern transition when perturbed locally at an appropriate frequency [1]. The switching from a globally disordered pattern of low mean amplitude to a globally ordered pattern of traveling excitation waves can be used for the “detection” of the perturbation frequency. To do this one can simply record the induced excitations, i.e. the suprathreshold firing of one of the model’s elements. A related detection principle is exploited in the time series analysis performed by the ear (see e.g. [2]). In the mammalian inner ear, for example, sound- induced mechanical vibrations are converted into sequences of nerve cell firings that propagate as excitation waves to the auditory cortex. There, the temporal patterns of excitations are interpreted with high accuracy and noise-tolerance, in spite of the original sound signal’s complexity and nonstationarity. The common assumption in the modeling of this process is that the spikes are induced from a resting state that is an excitable fixed point [3]. However, it was shown recently that bot