电压与钙耦合神经元模型的符号动力学

应用符号动力学研究了跨膜电压与细胞内钙浓度相耦合的R15神经元模型.通过峰峰间期序列(ISIs, Interspike Interval Series)的首归映射构造出描述周期和混沌放电模式的符号序列,并讨论了与切分岔密切联系的阵发混沌与嵌含在混沌区中的周期窗口的产生机理.由符号序列的排序规则,确定具有不同拓扑结构的放电节律与连续变化的参数值的对应关系,从而对实验或模型测得的任意放电模式进行参数识别.研究结果表明符号方法是研究神经放电活动动力学行为的一种有力工具.尤为重要的是,这样一种粗粒化的方法能够推广到神经电生理实验中,从复杂的实验数据中提炼更多有价值的信息. 

Symbolic dynamics of coupled neuron model of calcium and voltage

The R15 neuron model with the intracellular calcium concentrations coupled to the transmembrane voltage was studied by the symbolic dynamics.The symbolic expressions of periodic and chaotic firing patterns were constructed through the first-return maps of ISIs(interspike interval series).And also the intermittent chaos close correlative to the fold bifurcation and the generating mechanism of periodic windows embedded in the chaos region were discussed.The corresponding relation between firing rhythms with different topological structures and continuously varying parameter values was revealed on the basis of ordering rules of symbolic sequences.The corresponding parameter value of some firing pattern measured from the electrophysiological experiment or simulated by the mathematical model could be approximately fixed according to the ordering relation.Results show that symbolic approach is a powerful tool to study neural firing activities.In particular,such a coarse-grained way can be generalized in neural electrophysiological experiments to extract more valuable information from complicated experiment data.