Synthesis of an Equivalent Circuit for Spike-Timing-Dependent Axon Growth: What Fires Together Now Really Wires Together

Hardware realizations of neuronal networks should also consider axon growth in addition to synaptic weight changes, because this accounts for an additional dynamic aspect due to the delayed signal transmission varying with the grown axon length. Our aim is to model axon growth by electrical circuits to enable a dynamic, self-organized topology formation, extending the state of the art hardware realizations. We start from a lossless transmission line whose underlying partial differential equations serve as a modeling of a locally distributed static axon. We then derive a memory-dependent axon model implementing a growth mechanism by utilizing the wave digital concept as a modeling tool based on mapping voltages and currents to wave quantities. The growth mechanism utilizes memristive Jaumann structures and can be seen as a fundamental building block enabling a spike-timing-dependent topology formation. Emulation results show that our approach offers an axon model with reconfigurable axon length capable of mimicking spike-timing-dependent axon growth. Moreover, we consider Pavlov's dog experiment to demonstrate the delay-based self-organized topology formation due to Hebbian learning in a small neuronal network.