Convergence and periodicity in a delayed network of neurons with threshold nonlinearity

Electronic Journal of Differential Equations

Volumn 2003, Issue , 2003, Pages 1-14

  Guo, Shangjiang ^a   Huang, Lihong ^a   Wu, Jianhong ^b  

^a HUNAN UNIVERSITY   (China)

^b YORK UNIVERSITY   (Canada)

Author keywords

Convergence; Feedback; McCulloch Pitts nonlinearity; Neural networks; One dimensional map; Periodic solution

Indexed keywords

EID: 3042582252     PISSN: 10726691     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. Y. Chen and J. Wu, Existence and attraction of phase-locked oscillation in delayed network of two neurons, Differential Integral Equations, 14 (2001), 1181-1236.
2. Y. Chen, J. Wu and T. Krisztin, Connection orbits from synchronous periodic solutions to phase-locked periodic solutions in a delay differential system, J. Differential Equations, 163 (2000), 130-173.
3. A. Destexhe, P. Gaspard, Bursting oscillations from a homoclinic tangency in a time delay system, Phys. Lett. A, 173 (1993), 386-391.
4. S. Guo, L. Huang and J.Wu, Regular Dynamics in a network of two neurons with all-or-none activation functions. to appear.
5. S. Guo, L. Huang and J. Wu, Global attractivity of a synchronized periodic orbit in a delayed network, J. Math. Anal. Appl., 281 (2003), 633-646.
6. S. Guo, L. Huang and L. Wang, Linear stability and Hopf bifurcation in a two-neuron network with three delays, to appear in Int. J. Bifur. Chaos.
7. J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional Differential Equations, New York: Springer-Verlag, 1993.
8. J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Natl. Acad. Sci. USA, 81 (1984), 3088-3092.
9. L. Huang and J. Wu, Dynamics of inhibitory artificial neural networks with threshold nonlinearity, Fields Institute Communications, 29 (2001), 235-243.
10. L. Huang and J. Wu, The role of threshold in preventing delay-induced oscillations of frustrated neural networks with McCulloch-Pitts nonlinearity, Int. J. Math. Game Theory and Algebra, 11 (2001), 71-100.
11. L. Olien, J. Belair, Bifurcations, stability and monotonicity properties of a delayed neural network model, Physica D, 102 (1997), 349-363.
12. K. Pakdaman, C. Grotta-Ragazzo, C. P. Malta, O. Arino and J. F. Vibert, Effect of delay on the boundary of the basin attraction in a system of two neurons, Neural Networks, 11 (1998) 509-519.
13. K. Pakdaman, C. Grotta-Ragazzo and C. P. Malta, Transient regime duration in continuous-time neural networks delays, Phys. Rev. E, 58 (1998), 3623-3627.
14. P. Z. Taboas, Periodic solutions of planar delay equation, Proc. Roy. Soc. Edinburgh, 116A (1990), 85-101.
15. J. Wei, S. Ruan, Stability and bifurcation in a neural network model with two delays, Physica D, 130 (1999), 255-272.