扩散耦合神经元振子的半无源性与同步
Semi-passivity and synchronization of diffusively coupled neuronal oscillators
摘要：
我们讨论的神经元振荡器，通过扩散耦合，即通过间隙连接线性耦合网络中的同步。特别是，我们提出了在这些网络中使用的半被动和被动系统的理论同步的充分条件。我们发现，基于电导的神经元模型的Hodgkin-Huxley，Morris-Lecar，和流行的减少模型的FitzHugh-Nagumo和Hindmarsh-Rose都满足半被动性质，即这样一个模型的状态轨迹保持振荡，但有界提供的（电）能量是有界的。因此，对于广泛的耦合配置，这些振荡器的网络保证拥有最终有界的解决方案。此外，我们证明了当耦合足够强时，振荡器变得同步。利用耦合\HR和\ML振荡器的计算机模拟证实了我们的理论结论。最后，我们讨论可能的“不稳定性”的扩散耦合引起的振荡器网络。
英文摘要：
We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance-based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled \HR and \ML oscillators. Finally we discuss possible "instabilities" in networks of oscillators induced by the diffusive coupling.
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