Front bifurcations in an excitatory neural network
Front bifurcations in an excitatory neural network
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DOI：
10.1137/s0036139903434481
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发表时间：
2004-01-01
影响因子：
1.9
通讯作者：
Folias, SE
中科院分区：
文献类型：
--
作者：
Bressloff, PC;Folias, SE
我们展示了如何一个一维的兴奋性神经网络可以表现出对称性破缺前分叉类似于反应扩散系统中发现的。这发生在一个均匀的网络时，一个固定的前面经历了叉分叉，导致双向波传播。我们分析的动力学在附近的前分叉使用摄动方法，我们建立了一个弱的输入不均匀性可以诱导固定前的Hopf不稳定性，导致形成的振荡前或呼吸。然后，我们进行了稳定性分析，在一个完全可解的模型，并使用此导出条件的振荡前超出弱输入制度。特别是，我们展示了如何波传播故障发生在一个大的固定输入的存在下，由于固定前的钉扎;随后减少输入的强度，然后通过一个霍普夫不稳定性的前面生成一个呼吸器。最后，我们推导出一个移动的输入的移动前锁定的条件，我们如何锁定取决于输入的幅度和速度。
We show how a one-dimensional excitatory neural network can exhibit a symmetry breaking front bifurcation analogous to that found in reaction diffusion systems. This occurs in a homogeneous network when a stationary front undergoes a pitchfork bifurcation leading to bidirectional wave propagation. We analyze the dynamics in a neighborhood of the front bifurcation using perturbation methods, and we establish that a weak input inhomogeneity can induce a Hopf instability of the stationary front, leading to the formation of an oscillatory front or breather. We then carry out a stability analysis of stationary fronts in an exactly solvable model and use this to derive conditions for oscillatory fronts beyond the weak input regime. In particular, we show how wave propagation failure occurs in the presence of a large stationary input due to the pinning of a stationary front; a subsequent reduction in the strength of the input then generates a breather via a Hopf instability of the front. Finally, we derive conditions for the locking of a traveling front to a moving input, and we show how locking depends on both the amplitude and velocity of the input.