Hopf bifurcation analysis in a synaptically coupled FHN neuron model with delays

[1]  A. Hodgkin,et al.  A quantitative description of membrane current and its application to conduction and excitation in nerve , 1952, The Journal of physiology.

[2]  R. FitzHugh.  Impulses and Physiological States in Theoretical Models of Nerve Membrane. , 1961, Biophysical journal.

[3]  S. Yoshizawa,et al.  An Active Pulse Transmission Line Simulating Nerve Axon , 1962, Proceedings of the IRE.

[4]  A. Bautin.  Qualitative investigation of a particular nonlinear system: PMM vol. 39, n≗ 4, 1975, pp. 633–641 , 1975 .

[5]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[6]  Jianhong Wu.  SYMMETRIC FUNCTIONAL DIFFERENTIAL EQUATIONS AND NEURAL NETWORKS WITH MEMORY , 1998 .

[7]  Jianhong Wu,et al.  Synchronization and stable phase-locking in a network of neurons with memory , 1999 .

[8]  S. Ruan,et al.  Stability and bifurcation in a neural network model with two delays , 1999 .

[9]  S. Ruan,et al.  On the zeros of a third degree exponential polynomial with applications to a delayed model for the control of testosterone secretion. , 2001, IMA journal of mathematics applied in medicine and biology.

[10]  Hiroshi Kawakami,et al.  Bifurcations in Synaptically Coupled BVP Neurons , 2001, Int. J. Bifurc. Chaos.

[11]  Lihong Huang,et al.  Hopf bifurcating periodic orbits in a ring of neurons with delays , 2003 .

[12]  S. Ruan,et al.  On the zeros of transcendental functions with applications to stability of delay differential equations with two delays , 2003 .

[13]  TETSUSHI UETA,et al.  Bifurcation in asymmetrically coupled BVP oscillators , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[14]  N. Buric,et al.  Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[16]  Mingzhou Ding,et al.  Transitions to synchrony in coupled bursting neurons. , 2004, Physical review letters.

[17]  Hiroshi Kawakami,et al.  Bifurcation and Chaos in Coupled BVP oscillators , 2004, Int. J. Bifurc. Chaos.

[18]  Xingfu Zou,et al.  Hopf bifurcation in bidirectional associative memory neural networks with delays: analysis and computation , 2004 .

[19]  S. A. Campbell,et al.  Stability and Synchronization of a Ring of Identical Cells with Delayed Coupling , 2004 .

[20]  M. Velarde,et al.  Bifurcation analysis and existence of periodic solutions in a simple neural network with delays. , 2004, Chaos.

[21]  Junjie Wei,et al.  On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays , 2005 .

[22]  Yuan Yuan,et al.  Synchronized Hopf bifurcation analysis in a neural network model with delays , 2005 .

[23]  Junjie Wei,et al.  Hopf bifurcation analysis in a tri-neuron network with time delay , 2008 .

[24]  Guanrong Chen,et al.  Bifurcation and synchronization of synaptically coupled FHN models with time delay , 2009 .

[25]  Lihong Huang,et al.  Stability and Hopf bifurcation analysis on a ring of four neurons with delays , 2009, Appl. Math. Comput..