Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays

  title={Stability, Bifurcation, and Multistability in a System of Two Coupled Neurons with Multiple Time Delays},
  author={Leslie P. Shayer and Sue Ann Campbell},
  journal={SIAM Journal of Applied Mathematics},
A system of delay differential equations representing a model for a pair of neurons with time-delayed connections between the neurons and time delayed feedback from each neuron to itself is studied. Conditions for the linear stability of the trivial solution of this system are represented in a parameter space consisting of the sum of the time delays between the elements and the product of the strengths of the connections between the elements. It is shown that the trivial fixed point may lose… CONTINUE READING

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Publications referenced by this paper.
Showing 1-10 of 37 references

Neurons with graded response have collective computational properties like those of two-state neurons.

Proceedings of the National Academy of Sciences of the United States of America • 1984
View 4 Excerpts
Highly Influenced

Shayer,Analysis of a System of Two Coupled Neurons with Two Time Delays

L P.
Master’s thesis, University of Waterloo, ON, Canada, • 1998
View 3 Excerpts
Highly Influenced

XPPAUT3.0—The Differential Equations Tool

B. Ermentrout
University of Pittsburgh, Pittsburgh, • 1997
View 2 Excerpts
Highly Influenced

Time delay induced death in coupled limit cycle oscillators

D. R. Reddy, A. Sen, G. Johnston
Phys. Rev. Lett., 80 • 1998
View 1 Excerpt


L. Olien, J. Belair
stability, and monotonicity properties of a delayed neural network model, Phys. D, 102 • 1997
View 1 Excerpt

Transient oscillations in continuous-time excitatory ring neural networks with delay

K. Pakdaman, C. P. Malta, C. Grotta-Ragazzo, O. Arino, J.-F. Vibert
Phys. Rev. E, 55 • 1997

Delay induced periodicity in a neural netlet of excitation and inhibition

K. Gopalsamy, I. Leung
Phys. D, 89 • 1996
View 2 Excerpts

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