Multiple time-scale analysis of information representation for diverse learning rules among neurons

Abstract

Abstract Neural networks are complex systems in which multiple time-scale variables interact with each other, and how synaptic plasticity represents information related to firing activity is poorly understood. In this study, we constructed a synaptic plasticity model that considers physiological constraints by incorporating the strength of synaptic connections, dependent on the spike-timing-dependent plasticity (STDP) rule, into the voltage dependent theta neuron model. Next, we analyzed the multiple time-scale behaviors of the pulse-coupled oscillator system constructed using the synaptic plasticity model. The results show that the two-body system, which interacts by the product of conductance and potential difference, converges to the equilibrium point without chaotic solutions, that various coupling states are possible depending on the combination of learning rule and reversal potential values, that the number of clusters in the multi-body system can be predicted from the analysis results for the two-body system and that the final convergence point and vector field changed little for either excitatory or inhibitory neurons when the external current \(I\) was set to around the value at which the neuron spontaneously fires.