The code provided is designed to simulate neuronal networks and analyze their dynamics in a computational neuroscience framework. It focuses on two main types of models: weight-based and rate-based neuronal networks. Here is a biological basis of what the code is attempting to model: ## Biological Basis ### Weight-Based Perturbations - **Neural Connectivity:** - The `w_based_perturbation` function models the influence of altering synaptic weights on network dynamics. Biological synaptic weight changes can represent synaptic plasticity, such as Long-Term Potentiation (LTP) or Long-Term Depression (LTD), which are crucial for learning and memory. - **Influence Matrix:** - The function computes the influence of a perturbation on a specific neuron’s activity across the network. This is analogous to understanding the spread of an action potential or excitation across connected neural circuits due to a change in synaptic strength. ### Rate-Based Perturbations - **Neuronal Firing Rates:** - The `rate_based_perturbation` function simulates the effect of perturbing the input current, or external stimulus, to neurons in a rate-based network model. Neuronal firing rate models are commonly used to represent the average activity level of populations of neurons, which correlates with the average firing rate of biological neurons. - **Input Perturbations:** - The perturbations in input currents represent external stimuli or neuromodulatory changes that alter the firing rates of neurons. This can be related to sensory inputs or other environmental factors affecting neural states. - **Time Constants:** - The use of a time constant `tau` and differential equations to update the rate represents the temporal dynamics associated with neuron excitability and synaptic integration, mirroring processes such as membrane time constants in biological neurons. ### Dynamics and Nonlinearity - **Temporal Dynamics:** - The `simulate_dynamics` function integrates over time to simulate the network's temporal evolution. This mirrors the temporal dynamics of neuronal membrane potentials and spiking activity, adhering to the principles of electrophysiological properties of neurons. - **Nonlinearity and Rectification:** - The `NL` function applies a nonlinearity (rectification) to the input-output relationship of neurons. Biological neurons often exhibit nonlinear input-output functions, such as threshold behaviors, due to ion channel dynamics and synaptic integration. ### Noise - **Stochastic Influences:** - The inclusion of `noise` in the rate-based simulation mimics the inherent variability and stochastic nature of neuronal firing due to factors like synaptic noise and channel noise, which is essential for capturing the variability observed in biological neuron responses. In summary, the code models synaptic and neuronal network dynamics by simulating perturbations in synaptic weights and external inputs, capturing essential aspects of neuronal connectivity, plasticity, and firing rate dynamics observed in biological systems.