Abstract
Physiological evidences show that electrical activity affects a neuron’s neurite outgrowth by modulating the concentration of intra-cellular calcium (Kater et at., 1990). 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 dependant neurite growth in neural networks (van Ooyen and van Pelt, 1992; 1993). 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 behavior 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 a behavior.
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References
Kater, S.B., Guthrie, P.B. and Mills, L.R. (1990) Integration by the neuronal growth cone: a continum from neuroplasticity to neuropathology. Progress in Brain Research 86, 117–128.
van Ooyen, A. and van Pelt, J. (1992) Phase transitions, hysteresis and overshoot in developing neural networks. in Artificial Neural Networks, 2. I. Aleksander and J. Taylor (Eds). Elsevier Science Publishers B.V.
van Ooyen, A. and van Pelt, J. (1993) Activity-dependant outgrowth of neurons and overshoot phenomena in developing neural networks. Journal of Theoretical Biology, in press.
Zeeman E.C. (1972) Differential Equations for the Heartbeat and Nerve Impulse. Mathematics Institute University of Warwick Coventry, England.
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© 1994 Springer-Verlag London Limited
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Pakdaman, K., van Ooyen, A., Houweling, A.R., Vibert, JF. (1994). Hysteresis in a Two Neuron-Network: Basic Characteristics and Physiological Implications. In: Marinaro, M., Morasso, P.G. (eds) ICANN ’94. ICANN 1994. Springer, London. https://doi.org/10.1007/978-1-4471-2097-1_38
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DOI: https://doi.org/10.1007/978-1-4471-2097-1_38
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