In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system...In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.展开更多
利用正置双光子显微镜系统和荧光探针标记技术,观察脑内Ca2+分布,建立测量活体动物脑内Ca2+动态变化的实验方法。制作活体动物颅骨开窗样本,脑内负载Ca2+标记物Oregon Green 488 BAPTA-1和星型胶质细胞标记物Sulforhodamine 101,利用双...利用正置双光子显微镜系统和荧光探针标记技术,观察脑内Ca2+分布,建立测量活体动物脑内Ca2+动态变化的实验方法。制作活体动物颅骨开窗样本,脑内负载Ca2+标记物Oregon Green 488 BAPTA-1和星型胶质细胞标记物Sulforhodamine 101,利用双光子显微镜分别检测神经元和星型胶质细胞内Ca2+分布和动作电位引起的Ca2+瞬变。结果显示双光子显微镜可探测到脑内250μm处荧光信号,图像清晰且信噪比高,并能实时检测神经元和星型胶质细胞内Ca2+信号的动态变化。活体脑内Ca2+检测技术平台的建立为基础研究和医药应用提供了在体实验依据。展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11302126)the State Key Program of National Natural Science of China(Grant No.11032009)+1 种基金the Shanghai Leading Academic Discipline Project(Grant No.B302)Young Teacher Training Program of Colleges and Universities in Shanghai(Grant No.ZZhy12030)
文摘In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.
文摘利用正置双光子显微镜系统和荧光探针标记技术,观察脑内Ca2+分布,建立测量活体动物脑内Ca2+动态变化的实验方法。制作活体动物颅骨开窗样本,脑内负载Ca2+标记物Oregon Green 488 BAPTA-1和星型胶质细胞标记物Sulforhodamine 101,利用双光子显微镜分别检测神经元和星型胶质细胞内Ca2+分布和动作电位引起的Ca2+瞬变。结果显示双光子显微镜可探测到脑内250μm处荧光信号,图像清晰且信噪比高,并能实时检测神经元和星型胶质细胞内Ca2+信号的动态变化。活体脑内Ca2+检测技术平台的建立为基础研究和医药应用提供了在体实验依据。
