Homoclinic bifurcations at tonic-firing to bursting transitions: underlying mechanisms and impact on neuronal synchronization

我们提出了一系列的研究，以阐明生理合理的神经元模型的动力学特性。探索慢阈下电流在模型动力学中的作用，对于理解神经元从紧张性放电状态到爆发性放电状态的转变机制将起到至关重要的作用。这种转变似乎是与一种不寻常的同宿分岔的外观首次发现在这个模型。它的描述在分叉理论是我们提出的研究的一个中心方面。更现实的神经机制理论必须考虑噪声的作用。我们将通过将高斯白色噪声应用于离子流动力学来实现这一点，该离子流动力学导致膜电压的生理上合理的有色噪声扰动。由于神经元通常作为大型网络的一部分，我们将研究同步可以实现或破坏的情况和各种可能的场景。最近的研究表明，上述紧张到爆发的转变是建立或破坏同步的关键因素。我们的目标是找出如何以及为什么是这样的基础上，从我们的单神经元动力学的研究结果。

We propose a series of studies to elucidate the dynamical properties of a physiologically justified neuron model. Exploring the role of slow subthreshold currents in the model dynamics will play an essential role for understanding the mechanism of the neuron’s transition from a tonic firing state to a bursting state. This transition seems to be connected with the appearance of an unusual kind of homoclinic bifurcation first found in this model. Its description in terms of bifurcation theory is a central aspect of our proposed study. A more realistic theory of neuronal mechanisms has to take into account the role of noise. We will achieve this by applying Gaussian white noise to the ion flow kinetics which leads to a physiologically justifiable colored-noise perturbation of the membrane voltage. Since neurons usually act as parts of large networks, we will study the circumstances and various possible scenarios under which synchronization can be achieved or broken. Recent research hints at the aforementioned tonic-to-bursting transition to be the crucial ingredient that makes or breaks synchrony. We aim at finding out how and why this is so by building upon results obtained from our studies of the single-neuron dynamics.