On local bifurcations in neural field models with transmission delays.

@article{Gils2013OnLB,
  title={On local bifurcations in neural field models with transmission delays.},
  author={Stephan A. van Gils and Sophie Janssens and Y. A. Kuznetsov and S. Visser},
  journal={Journal of mathematical biology},
  year={2013},
  volume={66 4-5},
  pages={837-87}
}
Neural field models with transmission delays may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral… CONTINUE READING

From This Paper

Figures, tables, and topics from this paper.
6 Citations
29 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 29 references

A theory of linear delay differential equations in infinite dimensional spaces. In: Delay differential equations and applications

  • O Arino, E Sánchez
  • (NATO Sci. Ser. II Math. Phys. Chem.)
  • 2006
Highly Influential
9 Excerpts

Amplitude equations for systems with competing instabilities

  • PH Coullet, EA Spiegel
  • SIAM J Appl Math 43(4):776–821
  • 1983
Highly Influential
7 Excerpts

A class of abstract delay differential equations in the light of suns

  • SA Van Gils, SG Janssens
  • 2012
Highly Influential
4 Excerpts

Equations with infinite delay: blending the abstract and the concrete

  • O Diekmann, M Gyllenberg
  • J Differ Equ
  • 2012
1 Excerpt

A normalization technique for codimension two

  • SG Janssens, YuA Kuznetsov, O Diekmann
  • 2011
1 Excerpt

Similar Papers

Loading similar papers…