Coupled nonlinear oscillators are abundant in biological systems. In particular, oscillatory neurons play an important role in the human brain.
We investigate different architectures of coupled electrical oscillators for their suitability as parallel computing devices based on recent mathematical theories on weakly connected neural networks.
We are especially interested in dynamic coupling strategies that go beyond the classic excitatory and inhibitory coupling between neurons (i.e. the oscillators of our system). In a dynamically coupled network, part (or even all) of the information about the structure of the network is stored in the time dependence of the coupling rather than in the physical network topology.
Fig.1 shows an application, namely the "recognition" of a defective pixel pattern from a set of 3 memorized patterns in an experiment with 8 globally coupled electrical oscillators:
Global coupling here means that all neurons receive the same input from the coupling mechanism. Still, they react differently due to their inherently different oscillation frequencies. This approach simplifies building the network (Fig.2 shows the experimental circuit), but complicates providing the coupling signal.
Our main goal is to distribute the network complexity between the dynamic coupling and the network topology in a way that allows for the construction of large, efficient networks. A secondary goal is the theoretical understanding of the underlying dynamics and its application to pattern recognition.
K. Kostorz, R. W. Hölzel, K. Krischer, New J. Phys. 15, 083010 (2013)
R. W. Hölzel, K. Krischer, Physics Letters A, in press, DOI:10.1016/j.physleta.2013.08.02
R. W. Hölzel, K. Krischer, New J. Phys. 13 073031 (2011)