Abstract: A method for learning connections between nonlinear oscillators in a neural network comprising the steps of providing a plurality of nonlinear oscillators, with each respective oscillator producing an oscillation distinct from the others in response to an input and detecting an input at an at least first oscillator of the plurality of nonlinear oscillators. Detecting an input at an at least a second oscillator of the plurality of nonlinear oscillators, comparing the oscillation of the at least first oscillator to the oscillation of the at least second oscillator at a point in time, and determining whether there is coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator. Changing at least one of the amplitude and phase of a connection between the at least first oscillator and the at least second least oscillator as a function coherency between the at least first oscillator and the oscillation of the at least second oscillator.

Abstract: A method for mimicking the auditory system's response to rhythm of an input signal having a time varying structure comprising the steps of receiving a time varying input signal x(t) to a network of n nonlinear oscillators, each oscillator having a different natural frequency of oscillation and obeying a dynamical equation of the form r . = r ? ( ? + ? 1 ? ? z ? 2 + ? ? ? 2 ? ? z ? 4 1 - ? ? ? z ? 2 ) + c ? ? x ? ( t ) ? cos ? ? ? - r ? ? ? ? ? r 2 - 2 ? ? ? r ? ? cos ? ? ? + 1 ? . = ? + ? 1 ? r 2 + ? ? ? 2 ? r 4 1 - ? ? ? r 2 - c ? ? x ? ( t ) ? sin ? ( ? ) ? ? ? r 2 - 2 ? ? ? r ? ? cos ? ( ? ) + 1 ? ? ? . = - k ? ? x ? ( t ) ? sin ? ? ? ? ? ? r 2 - 2 ? ? ? r ? ? cos ? ? ? + 1 wherein ? represents the response frequency, r is the amplitude of the oscillator and ? is the phase of the oscillator.

Abstract: A method for mimicking the auditory system's response to rhythm of an input signal having a time varying structure comprising the steps of receiving a time varying input signal x(t) to a network of n nonlinear oscillators, each oscillator having a different natural frequency of oscillation and obeying a dynamical equation of the form r . = r ? ( ? + ? 1 ? ? z ? 2 + ? ? ? 2 ? ? z ? 4 1 - ? ? ? z ? 2 ) + c ? ? x ? ( t ) ? cos ? ? ? - r ? ? ? ? ? r 2 - 2 ? ? ? r ? ? cos ? ? ? + 1 ? . = ? + ? 1 ? r 2 + ? ? ? 2 ? r 4 1 - ? ? ? r 2 - c ? ? x ? ( t ) ? sin ? ( ? ) ? ? ? r 2 - 2 ? ? ? r ? ? cos ? ( ? ) + 1 ? ? ? . = - k ? ? x ? ( t ) ? sin ? ? ? ? ? ? r 2 - 2 ? ? ? r ? ? cos ? ? ? + 1 wherein ? represents the response frequency, r is the amplitude of the oscillator and ? is the phase of the oscillator.

Abstract: A method for learning connections between nonlinear oscillators in a neural network comprising the steps of providing a plurality of nonlinear oscillators, with each respective oscillator producing an oscillation distinct from the others in response to an input and detecting an input at an at least first oscillator of the plurality of nonlinear oscillators. Detecting an input at an at least a second oscillator of the plurality of nonlinear oscillators, comparing the oscillation of the at least first oscillator to the oscillation of the at least second oscillator at a point in time, and determining whether there is coherency between the oscillation of the at least first oscillator and the oscillation of the at least second oscillator. Changing at least one of the amplitude and phase of a connection between the at least first oscillator and the at least second least oscillator as a function coherency between the at least first oscillator and the oscillation of the at least second oscillator.

Abstract: The present invention is directed to systems and methods designed to ascertain the structure of acoustic signals. The approach involves an alternative transform of an acoustic input signal, utilizing a network of nonlinear oscillators in which each oscillator is tuned to a distinct frequency. Each oscillator receives input and interacts with the other oscillators in the network, yielding nonlinear resonances that are used to identify structure in an acoustic input signal. The output of the nonlinear frequency transform can be used as input to a system that will provide further analysis of the signal. According to one embodiment, the nonlinear responses are defined as a network of n expanded canonical oscillators zi, with an input, for each oscillator as a function of an external stimulus. In this way, the response of oscillators to inputs that are not close to its natural frequency are accounted for.