The provided code simulates a spiking neural network with inhibitory stabilization mechanisms, mimicking neural circuits observed in the brain that are tuned to a one-dimensional feature such as orientation. This setup is relevant to the understanding of biological circuits in sensory systems, especially in the visual cortex. ### Biological Basis 1. **Network Composition:** - **Excitatory and Inhibitory Neurons:** The network consists of 500 excitatory and 500 inhibitory neurons, a configuration that reflects the balanced nature of excitatory and inhibitory populations in cortical circuits. This balance is crucial for maintaining stable activity without runaway excitation or widespread inhibition. 2. **Neuron Model:** - **Leaky Integrate-and-Fire (LIF) Neurons:** The neurons are modeled using a simple LIF model. This model is characterized by its membrane potential dynamics that leak over time, mimicking the passive decay of the neuron's membrane potential in the absence of input. The neurons emit a spike when their potential reaches a threshold (\(vth = 20\)), after which they reset. This simplification captures essential spiking behavior observed in biological neurons. 3. **Synaptic Connectivity:** - **Synaptic Weights (JEE, JEI, JIE, JII):** The synaptic connections account for excitatory-to-excitatory (JEE), excitatory-to-inhibitory (JEI), inhibitory-to-excitatory (JIE), and inhibitory-to-inhibitory (JII) interactions. In the model, these interactions are modulated by factors (g = -2) and influence the network dynamics, reminiscent of how real synapses work to transmit excitatory or inhibitory signals. 4. **Tuning to Orientation:** - **Preferred Orientation (PO):** Each neuron has a randomly assigned preferred orientation within [0, π], which is analogous to the tuning properties of neurons in the visual cortex. In biological systems, neurons are known to respond preferentially to specific stimulus orientations, which is crucial for processing visual information. 5. **Activity Dynamics:** - **Perturbations and Rate Modulations:** The network simulates a patterned inhibitory perturbation based on feature similarity, allowing exploration of how perturbations affect activity patterns. This reflects how inhibitory neurons can influence overall network behavior, potentially stabilizing network dynamics and mediating sensory processing. 6. **Oscillatory Dynamics and Synaptic Plasticity:** - **Sinusoidal Modulation:** Sinusoidal functions (\(cos(2*(orientation difference))\)) are used to establish orientation-selective synaptic strength. This implies that neurons with similar orientation preferences are more strongly connected, fostering clustered activity patterns akin to those seen in orientation columns in the visual cortex. The model captures fundamental aspects of microcircuitry in the brain, particularly describing how excitation-inhibition balance and feature-tuned synaptic connectivity shape neuronal activity patterns. Such models are vital for understanding complex computations in sensory and cortical processing.