Evolution of periodic states and chaos in two types of neuronal models

摘要

Abstract: Studies on how chaos theory may be applied to neural disorders is a very challenging theoretical problem. But, to determine the applications of chaos theory cellular functions, it is best to study the genesis of chaos and its characteristics using a minimal model of cellular excitability. In this paper we present two neuronal models which gives rise to interesting types of bursting and chaos. The first model is based on the model of Chay, in which the bursting of neuronal cells is caused by voltage- and time-dependent inactivation of calcium channels. The second model is based on Chay's work in which the bursting is caused by the conformational transformation of the calcium channels that is induced by binding of Ca$+2$PLU$/ ion to the receptor site. With these two models, we elucidate how the periodic states and chaos can be evolved when the properties of two types of inward current change. Our bifurcation diagram reveals new types of bifurcations and chaos which were not seen in the other non-linear dynamic models. The predicted chaos from the models closely resembles that observed experimentally in neuronal cells. An implication of our finding is that chaos theory may be used to understand and improve the treatment of certain irregular activities in the brain.!23