The dynamics of an artificial neural network derived from a biological system, and its two applications to engineering problems are examined. The model has a multi-layer structure simulating the primary and secondary components in the olfactory system. The basic element in each layer is an oscillator which simulates the interactions between excitatory and inhibitory local neuron populations. Chaotic dynamics emerges from interactions within and between the layers, which are connected to each other by feedforward and feedback lines with distributed delays. A set of electroencephalogram (EEG) obtained from mammalian olfactory system yields aperiodic oscillation with 1/f characteristics in its FFT power spectrum. The EEG also reveals abrupt state transitions between a basal and an activated state. The activated state with each inhalation consists of a burst of oscillation at a common time-varying instantaneous frequency that is spatially amplitude-modulated (AM). The spatial pattern of the activated state seems to represent the class of the input ot the system, which simulates the input from sensory receptors. The KIII model of the olfactory system yields sustained aperiodic oscillation with "1/f" spectrum by adjustment of its parameters. Input in the form of a spatially distributed step funciton induces a state transition to an activated state. This property gives the model its utility in pattern classification. Four different methods (SD, RMS, PCA and FFT) were applied to extract AM patterns of the common output wave forms of the model. The pattern classification capability of the model was evaluated, and synchronization of the output wave form was shown to be crucial in PCA and FFT methods. This synchronization has also been suggested to have an important role in biological systems related to the information extraction by spatiotemporal integration of the output of a transmitting area of cortex by a receiving area.