Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators.
Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators.
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DOI：
10.1007/s10827-011-0315-2
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发表时间：
2011-10
影响因子：
1.2
通讯作者：
Canavier CC
中科院分区：
文献类型：
--
作者：
Woodman MM;Canavier CC
伽马振荡可以同步与近零相位滞后多个皮质区域和半球之间，以及在海马切片的两个远端站点之间。如何在长距离上以稳定的方式进行同步被认为是一个悬而未决的问题。相位复位曲线（PRC）跟踪输入提前或延迟下一个尖峰的程度，具体取决于在周期中接收到它的位置。我们使用PRCs脉动耦合的假设下，推导出1：1锁相的存在性和稳定性准则，该锁相是通过两个极限环振荡器的双向脉冲耦合产生的，对于任何1：1发射模式，具有任何持续时间的传导延迟。只要一个输入的影响在接收到下一个输入之前消散，耦合就可以很强。我们显示的形式，通用的同步和反相的解决方案采取的两个相同的，相同的脉冲耦合振荡器具有相同的延迟系统。稳定性判据具有简单的形式，其仅取决于接收输入的相位处的PRC的斜率和完成延迟反馈回路所需的周期数。完成延迟反馈回路所需的周期数取决于延迟值和触发模式。我们成功地在模型神经元网络上测试了我们方法的预测。该标准可以很容易地扩展到包括输入对接收到它的周期之后的周期的影响。
Gamma oscillations can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices. How synchronization can take place over long distances in a stable manner is considered an open question. The phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike, depending upon where in the cycle it is received. We use PRCs under the assumption of pulsatile coupling to derive existence and stability criteria for 1:1 phase-locking that arises via bidirectional pulse coupling of two limit cycle oscillators with a conduction delay of any duration for any 1:1 firing pattern. The coupling can be strong as long as the effect of one input dissipates before the next input is received. We show the form that the generic synchronous and anti-phase solutions take in a system of two identical, identically pulse-coupled oscillators with identical delays. The stability criterion has a simple form that depends only on the slopes of the PRCs at the phases at which inputs are received and on the number of cycles required to complete the delayed feedback loop. The number of cycles required to complete the delayed feedback loop depends upon both the value of the delay and the firing pattern. We successfully tested the predictions of our methods on networks of model neurons. The criteria can easily be extended to include the effect of an input on the cycle after the one in which it is received.
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影响因子：
8.6
作者：
Fischer, Ingo;Vicente, Raul;Garcia-Ojalvo, Jordi
通讯作者：
Garcia-Ojalvo, Jordi
影响因子：
8.6
作者：
Dhamala, M;Jirsa, VK;Ding, MZ
通讯作者：
Ding, MZ
影响因子：
1.9
作者：
Dror, R;Canavier, CC;Byrne, JH
通讯作者：
Byrne, JH
影响因子：
2.9
作者：
Karbowski, J;Kopell, N
通讯作者：
Kopell, N
影响因子：
2.9
作者：
ANDERSEN, P;SILFVENIUS, H;WIGSTROM, H
通讯作者：
WIGSTROM, H