Shared Inputs, Entrainment, and Desynchrony in Elliptic Bursters: From Slow Passage to Discontinuous Circle Maps
Shared Inputs, Entrainment, and Desynchrony in Elliptic Bursters: From Slow Passage to Discontinuous Circle Maps
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DOI：
10.1137/100811726
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发表时间：
2010-10
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影响因子：
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通讯作者：
Guillaume Lajoie;E. Shea-Brown
中科院分区：
文献类型：
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作者：
Guillaume Lajoie;E. Shea-Brown
在一组生物振荡器中，什么输入信号将导致同步与非同步？这个问题既与经典的夹带和锁相动力系统分析有关，也与控制神经网络活动的刺激模式的新兴研究有关。在这里，我们关注的是一群不耦合的椭圆爆裂神经元对一个共同脉冲输入的响应。我们从文献中扩展了相位缩减，以捕获不同强度的输入，从而得到一个具有不同阶次不连续的圆形图。在结合分析和数值的方法中，我们将我们的结果应用于椭圆破裂的范式模型和基底节区基于生物物理的神经元模型。我们发现，根据输入的周期和幅度，响应可以呈现混沌（相关的圆映射具有可证明的正Lyaponov指数），或者具有宽范围的锁相周期的周期性。在整个过程中，我们讨论了关键的潜在机制，包括通过Hopf分岔的慢通道效应，不连续的作用和起源，以及噪声的影响
What input signals will lead to synchrony vs. desynchrony in a group of biological oscillators? This question connects with both classical dynamical systems analyses of entrainment and phase locking and with emerging studies of stimulation patterns for controlling neural network activity. Here, we focus on the response of a population of uncoupled, elliptically bursting neurons to a common pulsatile input. We extend a phase reduction from the literature to capture inputs of varied strength, leading to a circle map with discontinuities of various orders. In a combined analytical and numerical approach, we apply our results to both a normal form model for elliptic bursting and to a biophysically-based neuron model from the basal ganglia. We find that, depending on the period and amplitude of inputs, the response can either appear chaotic (with provably positive Lyaponov exponent for the associated circle maps), or periodic with a broad range of phase-locked periods. Throughout, we discuss the critical underlying mechanisms, including slow-passage effects through Hopf bifurcation, the role and origin of discontinuities, and the impact of noise