The code provided is an implementation of a computational model based on the work by Nicolas Brunel in 2000, which is often referred to as the "Brunel network." This model is designed to simulate the dynamics of large networks of spiking neurons, particularly focusing on the balance between excitatory and inhibitory inputs that lead to different network states and collective firing patterns observed in the brain. ### Biological Basis 1. **Neuron Types and Integration**: - The network consists of two types of neurons: excitatory and inhibitory, reflecting a basic characteristic of cortical networks found in the brain. - Excitatory neurons (denoted as `N_E` in the code) make up 80% of the neurons, while inhibitory neurons (`N_I`) account for the remaining 20%. This ratio is common in many brain areas. - Neurons are modeled using leaky integrate-and-fire (LIF) units (`iaf_psc_delta`), which are simple models that capture the core behavior of real neurons: they integrate incoming synaptic inputs until their membrane potential reaches a threshold, eliciting a spike. 2. **Synaptic Interactions**: - The model includes both excitatory (`J_E`) and inhibitory (`J_I`) synapses. The weight of inhibitory synapses is set to be a multiple of the excitatory synapses (`g * J_E`), modeling the stronger effect of inhibitory inputs observed in biological networks. - Synaptic transmission incorporates a delay (`delay`), which mimics the propagation times found in real synapses. 3. **External Input**: - An external input to the network is simulated using a Poisson generator. This represents the random firing of external neurons that projects to the modeled network, often used to simulate sensory inputs or background brain activity. - The rate of external input is determined by `eta` and is scaled to match the firing rate that is sufficient to bring the neuron to its firing threshold (`V_th`). 4. **Membrane Dynamics**: - Neurons have a membrane time constant (`tau_m`), which is a crucial parameter influencing how quickly they integrate inputs compared to the timescale of synaptic currents. - The model utilizes dynamic randomization of initial membrane potentials to capture the variability seen in biological systems. 5. **Network Connectivity**: - Each neuron receives a fixed number of excitatory and inhibitory connections (`C_E` and `C_I`), reflecting the sparse and random connectivity pattern often observed in neural circuits. - The use of random distributions for synaptic weights introduces heterogeneity, a fundamental feature in neural systems that contributes to pattern diversity and network dynamics. ### Model Purpose The Brunel network model aims to explore how excitatory/inhibitory balances, synaptic delays, and connectivity patterns collectively influence the emergence of various dynamic states such as regular spiking, irregular firing, and asynchronous activity. These network dynamics are critical for understanding brain function, neural coding, and the regulation of information processing in neural circuits. By replicating the balance of excitation and inhibition, as well as the network architecture observed in actual cortical networks, the model serves as a foundational tool in the computational exploration of neural dynamics.