椭圆爆发中的共享输入、夹带和耗散：从慢通道到不连续圆映射
Shared inputs, entrainment, and desynchrony in elliptic bursters: from slow passage to discontinuous circle maps
摘要：
在一组生物振荡器中，什么样的输入信号会导致同步和不同步？这个问题与经典的动力系统分析的夹带和锁相和新兴的研究刺激模式控制神经网络的活动。在这里，我们专注于一个人口的非耦合，椭圆爆裂神经元的一个共同的脉动输入的反应。我们从文献中扩展了一个相位减少，以捕获不同强度的输入，从而导致各种顺序的不连续性的圆图。在结合分析和数值方法，我们将我们的研究结果应用到正常形式模型的椭圆爆发和生物神经元模型从基底神经节。我们发现，根据输入的周期和幅度，响应可以出现混沌（与相关的圆映射的可证明的正Lyaponov指数），或周期性的相位锁定周期的范围很广。在整个过程中，我们讨论了关键的基本机制，包括通过霍普夫分岔的慢通道效应，不连续性的作用和起源，以及噪声的影响
英文摘要：
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
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