# Biological Basis of the Computational Model The provided code represents a mean-field model of two interacting populations of Izhikevich neurons. Izhikevich neurons are a popular choice for simulating biologically plausible spiking neuron dynamics due to their ability to reproduce a wide array of neuron firing patterns while remaining computationally efficient. ## Key Biological Aspects ### Neuronal Populations - **Two Populations**: The code models two populations of neurons, each of which can be considered as a group of neurons with shared properties and interactions. ### Neuron Dynamics - **Mean-Field Approach**: The model uses a mean-field approach to simplify the interactions within and between populations by averaging the activity of all neurons in each population. - **State Variables**: For each population, there are variables `rm`, `vm`, `wm`, and `sm`, representing: - **Rate (rm)**: Reflects the firing rate of the population, capturing the averaged activity level of the neurons. - **Voltage (vm)**: Represents the membrane potential, indicating the level of electrical activity in the neurons. - **Adaptation Variable (wm)**: Corresponds to a mechanism that models spike-frequency adaptation, a biological process where a neuron's response to prolonged stimulation decreases over time. - **Synaptic Gating Variable (sm)**: Represents the synaptic strength or activity, which determines how the neurons communicate through synapses. ### Synaptic Interactions - **Synaptic Weights (gsyn)**: Parameters such as `gsyn11`, `gsyn12`, etc., model the synaptic strength between neurons within a population and between populations. - **Connections**: Functions `gs1(sm1, sm2)` and `gs2(sm1, sm2)` model the effective synaptic conductance considering the synaptic gating variables and predefined synaptic weights, representing the influence of one population on another. ### Parameters & Biological Constants - **Membrane Potential Dynamics**: Terms in `dvm/dt` equations represent key biological dynamics, including the intrinsic properties of the neurons (`alpha`, `er`) and external stimuli (`mu`, `Iext`). - **Synaptic and Adaptation Dynamics**: The adaptation and synaptic equations involve parameters (`a1, a2, tsyn, sjump`) that represent the timescales and magnitudes of synaptic plasticity and adaptation mechanisms. ### External Inputs - **External Currents (Iext1 and Iext2)**: Model the influence of external stimuli or inputs on the neuronal populations, common in simulations analyzing network responses to stimuli. ### Constraints - **Global Constraints**: Implement restrictions on variable values (e.g., `sm1`, `sm2`, `p1`) to ensure biological realism, such as synaptic variables remaining within physiological bounds ([0,1]). The model aims to simulate and understand the dynamics of interacting neuronal populations, including their response to stimuli and intra- and inter-population synaptic interactions. By capturing key elements of neuronal behavior and synaptic interactions, it bridges the gap between theoretical models and biological neurons' complex dynamics.