小世界神经元网络随机共振现象:混合突触和部分时滞的影响

实际神经元网络中,信息传递时电突触和化学突触同时存在,并且有些神经元间的时滞很小可以忽略.本文构建了带有不同类型突触耦合的小世界网络,研究部分时滞、混合突触及噪声对随机共振的影响.结果表明:兴奋性和抑制性突触的比例影响共振的产生;在抑制性突触为主的网络里,几乎不产生随机共振.系统最佳噪声强度和化学突触比例大致呈线性递增关系;特别是在以化学耦合为主的混合突触网络里,仅当兴奋性突触与抑制性突触比例约为4:1时,噪声才可诱导网络产生共振行为.在此比例下,引入部分时滞发现时滞可诱导网络产生随机多共振,且随网络中时滞边比例的增加,系统响应强度达到最优水平的时滞取值区间逐渐变窄;同时发现,网络中含有的化学突触越多,部分时滞诱导产生的多共振行为越强.此外,当时滞为系统固有周期的整数倍时,时滞越大共振所对应的噪声区域越广;并且网络中时滞边越多,越容易促使噪声和时滞诱导其产生明显的共振行为.     

生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声,特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的,但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡;(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳,说明了相干共振现象的发生. 关键词： 生物钟 分子噪声 日夜节律振荡 相干共振     

生物钟基因网络中分子噪声诱导的日夜节律振荡及相干共振

研究了果蝇细胞内生物钟基因调节网络的分子噪声，特别讨论了生物钟系统处于略微远离振荡区域的稳态时分子噪声对于时钟蛋白的日夜节律振荡的影响.结果表明：(1)虽然时钟蛋白合成或者衰减的生化反应事件是在随机的时间间隔里随机发生的，但系统可以依赖自身固有的调节机理诱导出明显的日夜节律振荡；(2)分子噪声诱导的日夜节律振荡的相干性可以在合适的分子噪声水平下到达最佳，说明了相干共振现象的发生.     

Influences of noise correlation and time delay on stochastic resonance induced by multiplicative signal in a cancer growth system

This paper investigates the stochastic resonance (SR) phenomenon induced by the multiplicative periodic signal in a cancer growth system with the cross-correlated noises and time delay. To describe the periodic change of the birth rate due to the periodic treatment, a multiplicative periodic signal is added to the system. Under the condition of small delay time, the analytical expression of the signal-to-noise ratio R_{\rm SNR} is derived in the adiabatic limit. By numerical calculation, the effects of the cross-correlation strength \lambda and the delay time \tau on R_{\rm SNR} are respectively discussed. The existence of a peak in the curves of R_{\rm SNR} as a function of the noise intensities indicates the occurrence of the SR phenomenon. It is found that \lambda and \tau play opposite role on the SR phenomenon, i.e., the SR is suppressed by increasing \lambda whereas it is enhanced with the increase of \tau, which is different from the case where the periodic signal is additive.     

Pattern transition and regulation in a subthalamopallidal network under electromagnetic effect

Although the significant roles of magnetic induction and electromagnetic radiation in the neural system have been widely studied, their influence on Parkinson's disease (PD) has yet to be well explored. By virtue of the magnetic flux variable, this paper studies the transition of firing patterns induced by magnetic induction and the regulation effect of external magnetic radiation on the firing activities of the subthalamopallidal network in basal ganglia. We find: (i) The network reproduces five typical waveforms corresponding to the severity of symptoms: weak cluster, episodic, continuous cluster, episodic, and continuous wave. (ii) Magnetic induction is a double-edged sword for the treatment of PD. Although the increase of magnetic coefficient may lead the physiological firing activity to transfer to pathological firing activity, it also can regulate the pathological intensity firing activity with excessive β-band power transferring to the physiological firing pattern with weak β-band power. (iii) External magnetic radiation could inhibit continuous tremulous firing and β-band power of subthalamic nucleus (STN), which means the severity of symptoms weakened. Especially, the bi-parameter plane of the regulation region shows that a short pulse period of magnetic radiation and a medium level of pulse percentage can well regulate pathological oscillation. This work helps to understand the firing activity of the subthalamopallidal network under electromagnetic effect. It may also provide insights into the mechanisms behind the electromagnetic therapy of PD-related firing activity.     

一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型的Hopf分岔与周期解问题

研究了一类具时滞的厄尔尼诺-南方涛动充电-放电振子模型. 给出了产生Hopf分岔的临界时滞条件, 利用Mawhin重合度理论,探讨了该模型的周期解问题. 关键词： 时滞 厄尔尼诺-南方涛动模型 Hopf分岔 周期解