Distributed Synaptic Connection Strength Changes Dynamics in a Population Firing Rate Model in Response to Continuous External Stimuli

Neural network complexity allows for diverse neuronal population dynamics and realizes higherorder brain functions such as cognition and memory. Complexity is enhanced through chemical synapses with exponentially decaying conductance and greater variation in the neuronal connection strength due to synaptic plasticity. However, in the macroscopic neuronal population model, synaptic connections are often described by spike connections, and connection strengths within the population are assumed to be uniform. Thus, the effects of synaptic connections variation on network synchronization remain unclear. Based on recent advances in mean field theory for the quadratic integrate-and-fire neuronal network model, we introduce synaptic conductance and variation of connection strength into the excitatory and inhibitory neuronal population model and derive the macroscopic firing rate equations for faithful modeling. We then introduce a heuristic switching rule of the dynamic system with respect to the mean membrane potentials to avoid divergences in the computation caused by variations in the neuronal connection strength. We show that the switching rule agrees with the numerical computation of the microscopic level model. In the derived model, variations in synaptic conductance and connection strength strongly alter the stability of the solutions to the equations, which is related to the mechanism of synchronous firing. When we apply physiologically plausible values from layer 4 of the mammalian primary visual cortex to the derived model, we observe event-related desynchronization at the alpha and beta frequencies and event-related synchronization at the gamma frequency over a wide range of balanced external currents. Our results show that the introduction of complex synaptic connections and physiologically valid numerical values into the low-dimensional mean field equations reproduces dynamic changes such as eventrelated (de)synchronization, and provides a unique mathematical insight into the relationship between synaptic strength variation and oscillatory mechanism.