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| 1 | Bifurcation analysis for Hindmarsh-Rose neuronal model with time-delayed feedback control and application to chaos control显示文摘This paper is concerned with bifurcations and chaos control of the Hindmarsh-Rose(HR)neuronal model with the time-delayed feedback control.By stability and bifurcation analysis,we find that the excitable neuron can emit spikes via the subcritical Hopf bifurcation,and exhibits periodic or chaotic spiking/bursting behaviors with the increase of external current.For the purpose of control of chaos,we adopt the time-delayed feedback control,and convert chaos control to the Hopf bifurcation of the delayed feedback system.Then the analytical conditions under which the Hopf bifurcation occurs are given with an explicit formula.Based on this,we show the Hopf bifurcation curves in the two-parameter plane.Finally,some numerical simulations are carried out to support the theoretical results.It is shown that by appropriate choice of feedback gain and time delay,the chaotic orbit can be controlled to be stable.The adopted method in this paper is general and can be applied to other neuronal models.It may help us better understand the bifurcation mechanisms of neural behaviors. | WANG HaiXia WANG QingYun ZHENG YanHong | 2014 | Science China(Technological Sciences)2014，57，5： | 18 |
| 2 | 频域两尺度簇发振荡结构及其动力学机制显示文摘以非自治杜芬-范德波尔振子为例,探讨了当外激励频率与系统固有频率之间存在量级差异,也即存在频域不同尺度时的快慢耦合效应。通过固定低频激励项,分析了快子系统的稳定性和分岔行为,得到了对应的两参数分岔集。将分岔集划分为5个区域,并分析了与各区域相关的簇发振荡模式。揭示了对称式折/折和对称式亚临界Hopf/亚临界Hopf等点-点式簇发的行为,以及对称式亚临界Hopf/极限环折和对称式延迟超临界Hopf/延迟超临界Hopf等点-圈式簇发的行为。研究结果表明:快子系统的多解和多分岔共存是诱发各种对称式簇发振荡模式的重要原因。 | 夏付兵 韩修静 瞿汭 毕勤胜 | 2017 | 河南科技大学学报(自然科学版)2017，38，4： | 2 |
| 3 | Complex bursting patterns in Van der Pol system with two slowly changing external forcings显示文摘This paper investigates the generation of complex bursting patterns in Van der Pol system with two slowly changing external forcings.Complex bursting patterns,including complex periodic bursting and chaotic bursting,are presented for the cases when the two frequencies are commensurate and incommensurate.These complex bursting patterns are novel and have not been reported in previous work.Based on the fast-slow dynamics,the evolution processes of the slow forcing are presented to reveal the dynamical mechanisms underlying the appearance of these complex bursting patterns.With the change of amplitudes and frequencies,the slow forcing may visit the spiking and rest areas in different ways,which leads to the generation of different complex bursting patterns. | HAN XiuJing BI QinSheng | 2012 | Science China(Technological Sciences)2012，55，3： | 2 |
| 4 | Morris-Lecar模型双参数分岔分析显示文摘Morris-Lecar(M-L)模型是一个重要的神经元模型.当适当调整参数时,M-L模型展示出许多复杂的动力学行为.文章针对M-L模型,利用双参数分岔分析并结合数值仿真的方法,研究了双参数平面上神经元电活动的存在区域及神经元电活动之间的转迁机制,实现了用同一个神经元模型模拟四种单参数分岔(超临界Hopf分岔、亚临界Hopf分岔、不变环上的鞍-结分岔和鞍同宿轨分岔)行为之间的转迁.同时,还考虑了在双参数分岔点附近极限环的幅值和共存区间的大小问题,为进一步研究分岔点附近的随机动力学机制提供了理论基础. | 卢裕木 丁学利 李群宏 | 2016 | 海南师范大学学报(自然科学版)2016，29，3： | 1 |
| 5 | 胰腺β细胞Bertram-Sherman模型中不同类型的簇放电模式显示文摘簇放电是胰岛素分泌放电活动的主要模式.本文主要针对具有快慢时间尺度的胰腺β细胞Bertram-Sherman模型,研究模型中参数变化时β细胞放电活动的变化类型,并通过快慢动力学分析方法对所产生的放电模式的产生机制和动力学行为进行解释. | 管亭亭 杨浩菊 | 2016 | 山西师范大学学报(自然科学版)2016，30，3： | 0 |
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