| In the brain, the recurrent architecture of the cortex is of critical importance to both its computational power, as well as to the generation of pathological conditions, such as epilepsy. A fundamental question in neuroscience is how the brain effectively harnesses the computational power of recurrent networks in which activity propagates in an internally generated fashion while creating behaviorally relevant spatiotemporal patterns of activity. I employ two homeostatic learning rules, termed synaptic scaling (SS) and presynaptic-dependent synaptic scaling (PSD), to study network dynamics in response to brief impulse stimuli. I find that the underling mathematical structures of these two rules are different in their transition matrix, which is diagonal as a linear mapping under usual matrix multiplication in the SS, but nondiagonal as a nonlinear mapping under the Hadamard product in the PSD. As a result, SS generates unstable dynamics with runaway excitation, but PSD provides stable dynamics. Then I conduct a systemic study of learning dynamics with biologically realistic neural networks consisted with spiking neurons and kinetic synapses. With more than one stimuli, multiple neural trajectories emerge in a self-organized manner. Using two measures in terms of graph theory, I find PSD generates a functionally feed-forward network when training with a single stimulus, and the complexity of network structure is increased in response to multiple stimuli. In addition, PSD and spike-timing-dependent plasticity (STDP) together improve the ability of the network to incorporate multiple and less variable trajectories. Using continuous neural dynamics, and defining a state vector to describe spike-timing patterns, I study several phenomena of memory dynamics. Finally, I study spontaneous neuron population activities under STDP. With the stimulated global EEG and local field potential, I find both satisfy the hierarchical symmetry across different scales with an exponent characterizing the degree of the balance of excitation and inhibition. |
