International Journal of Bifurcation and Chaos (2009) 19:1733-1739
Eugene M. Izhikevich and Frank C. Hoppensteadt
The Neurosciences Institute,
10640 John Jay Hopkins Drive,
San Diego, CA, 92121.
Abstract. There is great interest in methods for computing that do not involve digital machines. Many computational paradigms were inspired by brain research, such as Boolean neuronal logic, (McCulloch and Pitts 1943), the perceptron, (Rosenblatt 1958), attractor neural networks, (Hopfield 1982) and cellular neural nets (Chua and Yang 1988). All these paradigms abstract biological circuits to artificial neural networks, i.e., interconnected units (neurons) that perform computations based on the connections between the units (synapses). Here we present a novel computational framework based on polychronous wavefront dynamics. It is entirely different from an artificial neural network paradigm, rather it is based on temporal and spatial patterns of activity in pulse-propagating media and their interaction with transponders, which create pulses in response to receiving appropriate inputs, e.g., two coincident input pulses. A pulse propagates as a circular wave from its source to other transponders. Computations result from interactions between transponders, and they are encoded by the exact physical locations of transponders and by precise timings of pulses. We illustrate temporal pattern recognition, reverberating memory, temporal signal analysis, and basic logical operations using polychronous wavefront computations. This work reveals novel principles for designing nano-scale computational devices.
Full text in (pdf),
MATLAB GUI file polychrony.m, and a sample "memory 4" configuration memory4.mat