arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1002.4993cond-mat.dis-nn
收藏

无序神经网络中的集体振荡

Collective oscillations in disordered neural networks

Simona Olmi, Roberto Livi, Antonio Politi, Alessandro Torcini

摘要:

我们研究了在淬火和退火无序的存在下,脉冲耦合漏积分和点火神经元网络中集体振荡的发生。我们发现,无序诱导了一种弱形式的混沌,类似于有限数量N个振荡器的Kuramoto模型中出现的混沌[O. V. Popovych等人,E 71} 065201(R)(2005)]。事实上,当N趋于无穷大时,最大李雅普诺夫指数会趋于零,而这两种无序状态的指数是不同的。在热力学极限,随机网络动力学减少到一个完全均匀的系统与适当缩放的耦合强度。此外,我们还证明了周期性集体状态的李雅普诺夫谱以1/N^2的方式缩放到零,类似于“splay状态”的缩放。

英文摘要:

We investigate the onset of collective oscillations in a network of pulse-coupled leaky-integrate-and-fire neurons in the presence of quenched and annealed disorder. We find that the disorder induces a weak form of chaos that is analogous to that arising in the Kuramoto model for a finite number N of oscillators [O.V. Popovych at al., Phys. Rev. E 71} 065201(R) (2005)]. In fact, the maximum Lyapunov exponent turns out to scale to zero for N going to infinite, with an exponent that is different for the two types of disorder. In the thermodynamic limit, the random-network dynamics reduces to that of a fully homogenous system with a suitably scaled coupling strength. Moreover, we show that the Lyapunov spectrum of the periodically collective state scales to zero as 1/N^2, analogously to the scaling found for the `splay state'.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑