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Intermediate Stable Phase Locked States In Oscillator Networks

机译:振荡器网络中的中间稳定锁相状态

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摘要

The study of nonlinear oscillations is important in a variety of physical and biological contexts (especially in neuroscience).udSynchronization of oscillators has been a problem of interest in recent years. In networks of nearest neighbor coupled oscillators it is possible to obtain synchrony between oscillators, but also a variety of constant phase shifts between 0 and pi. We coin these phase shifts intermediate stable phase-locked states. In neuroscience, both individual neurons and populations of neurons can behave as complex nonlinear oscillators.ud Intermediate stable phase-locked states are shown to be obtainable between individual oscillators and populations of identical oscillators.These intermediate stable phase-locked states may be useful in the construction of central pattern generators: autonomous neural cicuits responsible for motor behavior. In large chains and two-dimenional arrays of oscillators, intermediate stable phase-locked states provide a mechanism to produce waves and patterns that cannot be obtained in traditional network models. A particular pattern of interest is known as an anti-wave. This pattern corresponds to the collision of two waves from opposite ends of an oscillator chain. This wave may be relevant in the spinal central pattern generators of various fish. Anti-wave solutions in both conductance based neuron models and phase oscillator models are analyzed. It is shown that such solutions arise in phase oscillator models in which the nonlinearity (interaction function) contains both higher order odd and even Fourier modes. These modes are prominent in pairs of synchronous oscillators which lose stability in a supercritical pitchfork bifurcation.ud
机译:非线性振荡的研究在各种物理和生物学环境(尤其是在神经科学领域)中都很重要。 ud近年来,振荡器的同步成为人们关注的问题。在最接近的相邻耦合振荡器的网络中,有可能获得振荡器之间的同步,但也可以获得0和pi之间的各种恒定相移。我们将这些相移称为中间稳定锁相状态。在神经科学中,单个神经元和神经元群体都可以充当复杂的非线性振荡器。 ud表明在单个振荡器和相同振荡器群之间可以获得中间稳定锁相态。这些中间稳定锁相态可能对中央模式发生器的构建:负责运动行为的自主神经回路。在大型链和二维振荡器阵列中,中间稳定的锁相态提供了一种机制,可以产生在传统网络模型中无法获得的波形和模式。感兴趣的特定模式被称为反波。该模式对应于来自振荡器链相对两端的两个波的碰撞。该波可能与各种鱼类的脊柱中央模式生成器有关。分析了基于电导的神经元模型和相位振荡器模型中的反波解决方案。结果表明,这种解决方案出现在相位振荡器模型中,其中非线性(相互作用函数)包含高阶奇数和偶数傅里叶模式。这些模式在成对的同步振荡器中很突出,这些同步振荡器在超临界干草叉分叉中失去稳定性。

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    Urban Alexander;

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  • 年度 2012
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