Tan Teck Liang, Cheong Siew Ann
Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371, Republic of Singapore.
Complexity Institute, Nanyang Technological University, Block 2 Innovation Centre, Level 2 Unit 245, 18 Nanyang Drive, Singapore 637723, Republic of Singapore.
PLoS One. 2017 Aug 29;12(8):e0183918. doi: 10.1371/journal.pone.0183918. eCollection 2017.
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 to the parameters of other neurons, so that the neuron dynamics can drive transitions from one phase to another on an artificial energy landscape. Finally, we measure the statistical complexity of the parameter time series, while the network is tuned from a regular network to a random network using the Watts-Strogatz rewiring algorithm. We find that the statistical complexity of the parameter dynamics is maximized when the neuron network is most small-world-like. Our results suggest that the small-world architecture of neuron connections in brains is not accidental, but may be related to the information processing that they do.
在本文中，我们研究了一个由Izhikevich神经元组成的网络，以探索大脑处于混沌边缘意味着什么。为此，我们首先构建了单个Izhikevich兴奋性神经元的相图，并在参数空间中确定了一个小区域，在该区域我们发现了大量的相边界，将其作为我们的混沌边缘。然后，我们将这些神经元的输出直接耦合到其他神经元的参数上，以便神经元动力学能够在人工能量景观上驱动从一个相到另一个相的转变。最后，我们测量参数时间序列的统计复杂性，同时使用Watts-Strogatz重连算法将网络从规则网络调整为随机网络。我们发现，当神经元网络最具小世界特性时，参数动力学的统计复杂性最大。我们的结果表明，大脑中神经元连接的小世界结构并非偶然，而是可能与它们所进行的信息处理有关。
