The provided MATLAB code is a computational model of neuronal phase oscillators, often employed in computational neuroscience to study the dynamics of neural networks. The model focuses on how neurons synchronize their firing and how network dynamics can be influenced by various parameters. ### Biological Basis #### Neuronal Oscillators - **Phase Oscillator Model**: Each neuron in the model is treated as a phase oscillator. This means that instead of modeling the detailed membrane potentials and ion channel dynamics of neurons, the model abstractly represents neurons by their phase (a value between 0 and 1) in the oscillation cycle. This approach simplifies the complexity of neuronal modeling while capturing essential aspects of rhythmic activity and synchronization. #### Components and Parameters - **Population and Connectivity**: The model involves `N = 100` neurons, with a high connectivity probability (`p_connect = 0.75`). This reflects the dense connectivity typical of some neural circuits, although it simplifies to binary connectivity without considering synapse heterogeneity or plasticity. - **Phase Resetting Curve (PRC)**: The phase reset concept, which is a key aspect of how oscillators respond to perturbations, is influenced by `amp0` and `amp1`. The Phase Resetting Curve represents how an incoming signal or perturbation shifts the timing of a neuron's next spike, affecting its phase. - **Synaptic Conductance**: Modeled by the parameter `amp2`, synaptic conductance represents the influence of incoming spikes on a neuron's phase progression. This is a simplified representation of synaptic input without distinguishing between excitatory and inhibitory effects. - **Noise and Adaptation**: The parameter `sigma0` represents stochastic noise in the neuronal firing process, which is biologically relevant as neurons often exhibit variability due to intrinsic and extrinsic noise. The model includes Ornstein-Uhlenbeck processes to simulate this noise, which aligns with the stochastic nature of biological synaptic input. #### Network Dynamics - **Coupling and Delay**: The coupling matrix `M`, scaled by `amp2`, depicts the strength and delay (`tau_del`) in synaptic interaction between neurons. Biological neurons communicate via synaptic transmission which often includes a delay, and the model captures this aspect to reflect more realistic synaptic timing. - **Theta Dynamics**: The core update rule for neuronal phases (`theta`) includes contributions from intrinsic oscillation (`omega`), synaptic inputs, and noise. Biological neurons also integrate multiple inputs, adjusting their spiking behavior accordingly. #### Biological Synonyms - **Sintegration and Synaptic Plasticity**: Though not detailed, the model implicitly takes into account the effects of synaptic integration over time, akin to the biological processes of facilitation and depression that occur in actual neural networks. In summary, the provided code models a network of phase-coupled oscillators, abstractly simulating core aspects of neuronal synchronization, synaptic coupling, and stochastic firing, which are all biologically grounded phenomena.