The provided code simulates a network of neurons to explore the relationship between oscillation frequencies, spike timing, and neural network coordination. Below is a description of how the code relates to biological concepts in computational neuroscience: ### Neuron Dynamics 1. **Izhikevich Neuron Model**: - The code is based on the Izhikevich neuron model, which is a simplified model used to replicate a diverse array of neuronal firing patterns with minimal computational cost. This model is characterized primarily by two state variables: membrane potential (`voltages`) and recovery variable (`u`), which together describe the excitability and spike generation of neurons. 2. **Neuron Types**: - The network consists of excitatory and inhibitory neurons, mimicking the balance of these neuron types found in the brain. The `pInhibitory` parameter sets the proportion of inhibitory neurons, affecting the overall dynamics and rhythmic activity of the network. 3. **Subthreshold Membrane Potential Dynamics**: - Parameters `a`, `b`, `restingVoltage`, and `d` in the code relate to the neuron's subthreshold dynamics and recovery rate, which together model how real neurons respond to input and return to their resting state after spiking. ### Network Connectivity and Synaptic Integration 1. **Synaptic Weight Matrix (`S`)**: - The synaptic weight matrix `S` determines the strength and nature of interactions between neurons. Positive weights correspond to excitatory connections, while negative weights represent inhibitory synapses, reflecting the biological reality of synaptic integration in neuronal networks. 2. **External Input (`inputz`)**: - The simulation of long-range inputs (`inputz`) models how external stimuli can influence neuronal networks. These inputs vary in strength and are introduced to study their impact on network oscillations, akin to sensory inputs or neuromodulatory signals in biological systems. ### Oscillatory Dynamics 1. **Gamma and Alpha Oscillations**: - The code measures oscillatory power in gamma (35-90 Hz) and alpha (5-15 Hz) bands. Gamma oscillations are often associated with cognitive functions such as attention and memory, while alpha oscillations are linked to relaxation and idling states of the brain. 2. **Power Spectral Density (PSD)**: - The Fourier Transform of mean excitatory neuron activity (`fireall`) forms a power spectral density (`ftz`), enabling the analysis of how network activity distributes across different frequency bands, reflecting complex interactions in neuronal circuits. ### Biological Relevance The simulation models biologically realistic phenomena like synaptic integration, excitation-inhibition balance, and rhythmic brain activity. These elements are fundamental in understanding neural circuit coordination and computational properties of the brain. By analyzing how oscillation frequencies affect spike timing and network behavior, the code provides insights into the dynamic processes underlying cognitive functions and neural computations in the brain.