The provided code simulates a network of neurons to explore fluctuations in oscillation frequency and their control over spike timing, relevant to coordinating neural networks. This model is inspired by the work of M.X. Cohen and based on Izhikevich’s neural model principles. ### Key Biological Concepts Modeled 1. **Neuron Types and Composition**: - The simulation includes two types of neurons: excitatory (800) and inhibitory (200), reflecting the common cortical composition where excitatory neurons usually outnumber inhibitory neurons. 2. **Neuronal Dynamics**: - The neuronal behavior is governed by a simplified model resembling the Izhikevich model, which is derived from biological observations on membrane potential dynamics. - The parameters used (`a`, `b`, `c`, and `d`) define the equations for membrane potential and recovery variables. These parameters capture different firing patterns and types of neurons observed in biology. Inhibitory neuron parameters show variability through random adjustments (`ri1`, `ri2`, `ri3`), akin to biological diversity. 3. **Membrane Potential and Spike Generation**: - Neuronal voltages start at a resting potential and evolve over time based on input current and the recovery variable `u`, which models the effect of ion concentrations such as potassium on neuronal excitability. - A neuron fires when its membrane potential reaches a certain threshold (30 mV). The model resets the neuron’s potential mimicking the cycle of depolarization and repolarization. 4. **Synaptic Inputs**: - The neural network’s interactions are defined using connectivity matrices (`S1`, `S2`, `S3`) that simulate synaptic inputs, with positive weights representing excitatory and negative weights representing inhibitory connections, common in biological synapses. - Inputs vary due to an externally specified signal (`inputstrength`) and a sinusoidal variation to model the impact of external rhythmic drives such as those observed in cognitive and sensory processing. 5. **Oscillations and Signal Filtering**: - The model targets gamma frequency oscillations (40-90 Hz), which are important for cognitive functions and often show coherent rhythms across networks. - Hilbert transforms and frequency analysis techniques are used to extract phase information reflecting neuronal oscillatory activity, highlighting the relevance of oscillations for network communication and temporal coordination. 6. **Frequency Sliding/Drift**: - The simulation evaluates how the phase of neural oscillations changes over time, a phenomena related to the dynamic modulation of network connectivity and neural communication. ### Conclusion This code models the dynamic interactions and oscillatory behaviors of cortical networks, focusing on the fluctuations in oscillation frequency and their impact on spike timing—both critical for understanding neural coding, synchronization, and the coordination of large-scale brain processes such as perception and attention.