Bashkirtseva Irina, Ryashko Lev, Slepukhina Evdokia
Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, Ekaterinburg, Russia.
Phys Rev E. 2019 Jun;99(6-1):062408. doi: 10.1103/PhysRevE.99.062408.
We study a special variant of the noise-induced transition between spiking and bursting regimes associated with the blue sky catastrophe bifurcation in the Hindmarsh-Rose neuron model. We show that in the parameter region close to the bifurcation value, where the only attractor of the system is the limit cycle of tonic spiking type, noise can transform the spiking oscillatory regime to the bursting one. This phenomenon is studied by means of power spectral density and interspike intervals statistics. We show that noise shifts the bifurcation value, so that bursting activity can be observed for a wider parameter range. Moreover, we reveal that the stochastic spiking-bursting transitions in this system are accompanied by the change in sign of the Lyapunov exponent. We perform a detailed quantitative analysis of these phenomena with an approach that uses a concept of the stochastic sensitivity function, the confidence domains method, and Mahalanobis metrics.
我们研究了与Hindmarsh-Rose神经元模型中蓝天灾难分岔相关的尖峰和爆发状态之间噪声诱导转变的一种特殊变体。我们表明，在接近分岔值的参数区域，系统的唯一吸引子是强直尖峰类型的极限环，噪声可以将尖峰振荡状态转变为爆发状态。通过功率谱密度和峰峰间隔统计来研究这一现象。我们表明，噪声会使分岔值发生偏移，从而在更宽的参数范围内可以观察到爆发活动。此外，我们揭示了该系统中的随机尖峰-爆发转变伴随着李雅普诺夫指数符号的变化。我们使用随机灵敏度函数的概念、置信域方法和马氏距离度量，对这些现象进行了详细的定量分析。
