### Biological Basis of the Code This code is designed to simulate the network dynamics of excitatory neurons using a mean-field approximation. The biological model attempts to capture aspects of synaptic interactions and neuronal firing rates in a simplified computational framework. Below are key biological elements that the code tries to model: #### Neuronal Population - **Neuron Type**: The model explicitly focuses on simulating a network of excitatory neurons, specifically Integrate-and-Fire (IeF) neurons. These neurons are commonly used in computational studies to mimic the firing behavior of real neurons based on simple integrate-and-fire dynamics. - **Network Size**: The code simulates a network of 100 neurons. While this is a relatively small number compared to the thousands found in real brain circuits, it allows for the basic exploration of network dynamics. #### Synaptic Connectivity - **Connection Probability (C)**: The code models synapses with a probability of connection, `C`, which ranges in this exploration from 0.1 to 0.5. This reflects the sparsity of synaptic connections found in many parts of the brain, where not every neuron is directly connected to every other neuron. - **Synaptic Efficacy (J)**: The mean synaptic efficacy or average synaptic strength (`J`) is set to 22 picoamperes (pA). This parameter reflects the amplitude of the excitatory postsynaptic current (EPSC) per synapse, a pivotal factor influencing neuronal excitability and synchrony. #### Synaptic Plasticity and Noise - **Short-term Synaptic Plasticity (U)**: The code includes a parameter `U` that represents the presynaptic probability of neurotransmitter release, set at 50%, indicating that the model incorporates aspects of short-term synaptic plasticity. This reflects the dynamic nature of synaptic transmission in actual neural tissue, where the likelihood of neurotransmitter release can increase or decrease over short time scales. - **Background Synaptic Release**: Parameters `m` and `s` account for constant and fluctuating components of synaptic input, respectively, simulating the ongoing background activity and noise present in the brain. #### Simulation Duration - **Simulation Duration (dsim)**: The model runs the simulation for 1 million milliseconds or 1000 seconds. This extended simulation time allows for the observation of stable patterns and variability in the network's activity over time, akin to observing real neural networks' behavior over similar durations. #### Output Analysis - **Spike Detection**: The simulation results are analyzed to detect spikes and bursts in neuronal activity, related to networks' firing patterns. The code computes inter-burst intervals (IBI) and uses these measures to examine network dynamics under varying connection probabilities. In summary, the code serves as a basic model to explore how varying synaptic connectivity and other parameters influence the behavior of excitatory neural networks, focusing on spike dynamics and synaptic interactions, crucial components in understanding neural circuit function in vivo.