Understanding the dynamic behavior of neuronal networks in silico is crucial for tackling analysis their biological counterparts and making accurate predictions. Of particular importance determining structural dynamical conditions necessary a network to activate spontaneously, transitioning from quiescent ensemble neurons network-wide coherent burst. Drawing versatility Master Stability Functio...

Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns understand working mechanism of brain activity, especially cortical areas. Here, we present an explicit mathematical analysis, corroborated by numerical results, identify investigate spatiotemporal, non-uniform, emerg...

In this paper, we study a network of Izhikevich neurons to explore what it means for a brain to be at the edge of chaos. To do so, we first constructed the phase diagram of a single Izhikevich excitatory neuron, and identified a small region of the parameter space where we find a large number of phase boundaries to serve as our edge of chaos. We then couple the outputs of these neurons directly...

In this paper we analyze simple computations with spiking neural networks (SNN), laying the foundation for more sophisticated calculations. We consider both a deterministic and a stochastic computation framework with SNNs, by utilizing the Izhikevich neuron model in various simulated experiments. Within the deterministic-computation framework, we design and implement fundamental mathematical op...

Spiking neural networks that have variable connection delays have the interesting property that they are sensitive to both spatial and temporal patterns of input. Each neuron in the network receives input from spatially-distributed input neurons whose precise firing times interact with connection delays to determine whether the neuron can exceed the firing threshold and produce an output. The n...