Mechanism of long transient oscillations in cyclic coupled systems
Mechanism of long transient oscillations in cyclic coupled systems
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DOI：
10.1016/j.chaos.2009.03.103
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发表时间：
2009-11
影响因子：
7.8
通讯作者：
H. Kitajima;Y. Horikawa
中科院分区：
文献类型：
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作者：
H. Kitajima;Y. Horikawa
我们考虑单向耦合环网络的神经元抑制连接。当抑制神经元个数为偶数时，系统不存在稳定的振荡模式。然而，我们在这种情况下观察到的振荡模式。在本文中，我们阐明了振荡机制的状态空间。我们研究这些振荡模式和不稳定的周期解（UPS）产生的Hopf分岔之间的关系。结果发现，这些瞬态振荡模式产生的轨迹接近UPS，并在它周围停留了很长一段时间。我们也证实了这种现象在一个简单的电路使用反相运算放大器。
We consider unidirectionally coupled ring networks of neurons with inhibitory connections. It is known that when a number of inhibitory neurons is even, the system never has stable oscillatory modes. However, we observed oscillatory modes in such a case. In this paper, we clarify the oscillation mechanism in a state space. We investigate the relationship between these oscillatory modes and the unstable periodic solutions (UPSs) generated by the Hopf bifurcations. As a result we find that these transient oscillatory modes are generated by trajectories closing to the UPS and staying around it for a long time. We also confirm this phenomenon in a simple electrical circuit using inverting operational amplifiers.