一类新的混沌神经放电的动力学特征的实验和数学模型研究

神经元电活动理论模型Hindmarsh-Rose(HR)模型提示有位于周期1和周期2放电模式之间的一类特殊的混沌放电,但长期以来对其没有获得足够认识.依据回归映射的确定性结构和非线性预报的短期可预报性,确认了在大鼠的实验性神经起步点的实验中发现的位于周期1和周期2放电模式之间的非周期放电是混沌放电模式,还将该混沌放电模式区分为3个不同表观样式.其中1个表观形式与HR模型的仿真结果相类似,验证了HR模型的理论预期;其余2个样式与仿真结果并不相似.进一步揭示了3个表观样式的动力学特征以及相互之间的区别与联系,并与位于周期2和周期3节律之间、周期3和周期4节律之间的混沌比较了异同,也区别了从周期1到混沌再到周期2放电模式的节律转迁历程与其他的从周期1到周期2节律的分岔过程的不同.研究结果确认了该类特殊混沌节律和相应分岔过程的新特征,丰富了混沌放电节律和节律分岔序列的种类.还对仿真该混沌的多样性和非光滑特性,以及揭示该类混沌的产生途径等进行了讨论. 关键词： 混沌 神经放电模式 分岔 节律

Dynamics of a novel chaotic neural firing pattern discovered in experiment and simulated in mathematical model

A special chaotic firing pattern lying between period-1 and period-2 firing pattern simulated in theoretical neuronal firing model, Hindmarsh-Rose (HR) model, has not been adequately understood for a long time. The non-periodic neural firing patterns lying between period-1 and period-2 firing pattern discovered in the biological experiments on neural pacemakers of rats are identified to be chaotic bursting and divided into three styles in appearance, according to the deterministic structures of the first return map and the short-term predictability of nonlinear predication. One style of the experimental chaos exhibits characteristics similar to the numerical simulations of the theoretical model, verifying the theoretical participation of HR model, while other styles display different characteristics. The characteristics of the three styles and the relationship and distinction among 3 styles of the chaotic rhythms are identified, and compared with those lying between period-2 and period-3 firing pattern, and between period-3 and period-4 firing pattern. In addition, the distinction between the transition procedure from period-1 to chaos and then to period-2 and other bifurcation scenarios from period-1 to period-2 firing pattern is also identified. The results confirm the novel chaos lying between period-1 and period-2 and the corresponding novel bifurcation scenario, enriching the kinds of the chaotic rhythms and bifurcation scenarios of neural firing. Finally simulations of the diversity and non-smooth characteristics of the chaotic rhythms discovered in the experiment and identification of the routine to chaos are also discussed.