Codes from Collective states in a ring network of theta neurons

We consider a ring network of theta neurons with non-local homogeneous coupling. We analyse the corresponding continuum evolution equation, analytically describing all possible steady states and their stability. By considering a number of different parameter sets, we determine the typical bifurcation scenarios of the network, and put on a rigorous footing some previously observed numerical results.

我们考虑一类带非局部均匀耦合的θ神经元（theta neuron）环形网络。针对该网络对应的连续体演化方程，我们展开解析分析，完整刻画了所有可能的稳态及其稳定性特征。通过考察多组不同的参数集合，我们明确了该网络的典型分岔场景，并为此前已观测到的部分数值结果奠定了严谨的理论基础。