Interaction dynamics in small networks of nonlinear elements

• Input–output relationship of a network of 1–2 elements (modeled as neurons) is studied.
• Excitatory and inhibitory input and feedforward and recurrent topologies are considered.
• For spiking neurons, we find locking, rate amplification and inhibiton-induced rate control.
• For chattering neurons, we find rate amplification for slow input and silencing for fast input.

We study a small circuit of coupled nonlinear elements to investigate general features of signal transmission through networks. The small circuit itself is perceived as building block for larger networks. Individual dynamics and coupling are motivated by neuronal systems: We consider two types of dynamical modes for an individual element, regular spiking and chattering and each individual element can receive excitatory and/or inhibitory inputs and is subjected to different feedback types (excitatory and inhibitory; forward and recurrent). Both, deterministic and stochastic simulations are carried out to study the input–output relationships of these networks. Major results for regular spiking elements include frequency locking, spike rate amplification for strong synaptic coupling, and inhibition-induced spike rate control which can be interpreted as a output frequency rectification. For chattering elements, spike rate amplification for low frequencies and silencing for large frequencies is characteristic.