Stability and Bifurcations in Neural Fields with Finite Propagation Speed and General Connectivity

@article{Atay2004StabilityAB,
  title={Stability and Bifurcations in Neural Fields with Finite Propagation Speed and General Connectivity},
  author={Fatihcan M. Atay and Axel Hutt},
  journal={SIAM Journal of Applied Mathematics},
  year={2004},
  volume={65},
  pages={644-666}
}
A stability analysis is presented for neural field equations in the presence of finite propagation speed along axons and for a general class of connectivity kernels and synaptic properties. Sufficient conditions are given for the stability of equilibrium solutions. It is shown that the propagation delays play a significant role in nonstationary bifurcations of equilibria, whereas the stationary bifurcations depend only on the connectivity kernel. In the case of nonstationary bifurcations… CONTINUE READING

Citations

Publications citing this paper.
Showing 1-10 of 36 extracted citations

Analysis of nonlocal neural fields for both general and gamma-distributed connectivities

Axel Hutta, Fatihcan M. Atayb
2005
View 5 Excerpts
Highly Influenced

References

Publications referenced by this paper.
Showing 1-10 of 53 references

Physics of the extended neuron

P. C. Bressloff, S. Coombes
Internat. J. Modern Phys. B, 11 • 1997
View 4 Excerpts
Highly Influenced

Activity dynamics in nonlocal interacting neural fields.

Physical review. E, Statistical, nonlinear, and soft matter physics • 2003
View 1 Excerpt

Synchronization in oscillator networks with delayed coupling: a stability criterion.

Physical review. E, Statistical, nonlinear, and soft matter physics • 2003
View 1 Excerpt

Modeling collective excitations in cortical tissue

W. M. Kistler, R. Seitz, J. L. van Hemmen
Phys . D • 2002

Similar Papers

Loading similar papers…