Neural Network STDP Simulation
        
            About this simulation:
            This simulation models spike-timing dependent plasticity (STDP) in a neural network with excitatory and inhibitory neurons using mean-field theory. The key equations being simulated are:
         
        
            Key Equations
            
            
                1. Firing Rate Dynamics
                
                    τr 
                        
                            d𝐫⃗
                            dt
                        
                     = -𝐫 + 𝕎𝐫 + 𝕎X𝐫X
                
                
                    Where 𝐫 = [rE, rI] are the excitatory and inhibitory firing rates
                
             
            
                2. Connectivity Matrices
                
                    𝕎 = (
                        (NE-1)wEE    -NIwEI
                        NEwIE    -(NI-1)wII
                    )
                
                
                    𝕎X = Nx (
                        wEX    0
                        0    wIX
                    )
                
                
                    𝐫X = [aE, aI] are the external drive parameters
                
             
            
                3. STDP Weight Evolution
                
                    
                        
                            d𝑤EE
                            dt
                        
                     = (τSTDP/τwEE) rE(rE - b)
                
                
                    
                        
                            d𝑤EI
                            dt
                        
                     = (τSTDP/τwEI) rI(rE - b)
                
                
                    Synaptic weights evolve based on pre- and post-synaptic activity with threshold b
                
             
         
        
        
            Typical parameter combinations to try:
            
                - σ = 0.1, aE = 20, wEE = 10, wEI = 10, Time = 10s (standard)
 
                - σ = 0.3, aE = 30, wEE = 10, wEI = 10, Time = 20s (higher activity)
 
                - σ = 0.0, aE = 15, wEE = 10, wEI = 10, Time = 50s (no noise, longer)
 
                - σ = 0.5, aE = 25, wEE = 10, wEI = 10, Time = 30s (high noise)