Hysteresis in a two-neuron network: basic characteristics and physiological implications
Pakdaman, K., Van Ooyen, A., Houweling, A. R., and Vibert, J.-F. (1994). In: Marinaro, M., and Morasso, P. G., eds. Artificial Neural Networks - ICANN 1994, 4th International Conference on Artificial Neural Networks, Sorrento, Italy, pp. 162-165. [Full text: PDF]
Physiological evidences show that electrical activity affects a neuron's neurite outgrowth by modulating the concentration of intra-cellular calcium. The change of connectivity thus produced modifies in turn the electrical activity. Based upon such evidences, van Ooyen and van Pelt devised a model for activity-dependent neurite outgrowth. Their study shows that when the neuron model has a sigmoidal transfer function with a spontaneous activity, the network connectivity goes through an overshoot followed by elimination before stabilizing. This behaviour was explained by the activity being a hysteresis function of connectivity. In this paper we further investigate the basic characteristics required for the network activity to display such behaviour.