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首页> 外文期刊>Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics >Multirhythmicity generated by slow variable diffusion in a ring of relaxation oscillators and noise-induced abnormal interspike variability - art. no. 046232
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Multirhythmicity generated by slow variable diffusion in a ring of relaxation oscillators and noise-induced abnormal interspike variability - art. no. 046232

机译：由松弛振荡器环中的缓慢变量扩散和噪声引起的异常峰值间变异性产生的多节奏性-艺术。没有。 046232

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摘要

The deterministic and noise-dependent dynamics of a ring of three Ohmically coupled electronic relaxation oscillators are considered by means of numerical simulations. Each isolated oscillator is described by a set of two ordinary differential equations with very different characteristic times. The emergence of the limit cycle via the Hopf bifurcation results from the N-shaped current-versus-voltage characteristic of the nonlinear resistor. The phase diagram is calculated for a ring of three such oscillators in the presence of small detuning. Special attention is focused on two parameter areas, one near a transition to the homogeneous and the other near the inhomogeneous stable steady state. Along with other nontrivial limit cycles, essentially asymmetrical limit cycles termed dynamic traps may arise in these two areas. A dynamic trap is a regime in which one or two oscillators do not perform full-amplitude oscillations and, correspondingly, do not generate spikes. The interspike interval (ISI) distribution in the presence of noise is calculated as a function of the coupling strength in both areas of the parameter plane. The distributions are extremely polymodal near the homogeneous steady state even if the in-phase limit cycle is dominating. The origins of this abnormal enhancement of ISI variability are discussed in detail. A similar analysis shows that nontrivial periodic attractors are observable in the vicinity of the inhomogeneous stable steady states only if the level of noise is relatively low. In this case, the dominance of the in-phase limit cycle basin results in an almost unimodal distribution of interspike intervals. [References: 39]
机译：通过数值模拟考虑了三个欧姆耦合电子张弛振荡器环的确定性和噪声相关动力学。每个隔离的振荡器由两个具有不同特征时间的常微分方程组描述。通过Hopf分叉出现极限循环的原因是非线性电阻的N形电流-电压特性。在存在小的失谐情况下，针对三个这样的振荡器的环计算相位图。特别注意的是两个参数区域，一个靠近过渡到均匀状态，另一个靠近非均匀稳定状态。与其他非平凡的极限环一起，在这两个区域中可能会出现本质上不对称的极限环，称为动态陷阱。动态陷阱是一种状态，其中一个或两个振荡器不执行全振幅振荡，并且相应地，不产生尖峰。计算存在噪声时的尖峰间间隔（ISI），作为参数平面两个区域中耦合强度的函数。即使同相极限循环占主导地位，在均质稳态附近，分布仍是多峰的。 ISI变异性的这种异常增强的起因已详细讨论。类似的分析表明，只有在噪声水平相对较低的情况下，在非均匀稳定稳态附近才能观察到非平凡的周期性吸引子。在这种情况下，同相极限循环盆地的主导地位导致尖峰间间隔的几乎单峰分布。 [参考：39]

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