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Stability of synchronous oscillations in a system of Hodgkin-Huxley neurons with delayed diffusive and pulsed coupling

Enrico Rossoni*

Yonghong Chen and Mingzhou Ding

Jianfeng Feng†

  • Department of Informatics, Sussex University, Brighton BN1 9QH, United Kingdom

  • Department of Biomedical Engineering, University of Florida, Gainesville, Florida 32611, USA

  • Department of Mathematics, Hunan Normal University, 410081 Changsha, People's Republic of China
  • and Department of Computer Science, Warwick University, Coventry CV4 7AL, United Kingdom

  • *Electronic address: e.rossoni@sussex.ac.uk
  • †Electronic address: jianfeng.feng@warwick.ac.uk
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Phys. Rev. E 71, 061904 – Published 9 June, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.061904

Abstract

We study the synchronization dynamics for a system of two Hodgkin-Huxley (HH) neurons coupled diffusively or through pulselike interactions. By calculating the maximum transverse Lyapunov exponent, we found that, with diffusive coupling, there are three regions in the parameter space, corresponding to qualitatively distinct behaviors of the coupled dynamics. In particular, the two neurons can synchronize in two regions and desynchronize in the third. When excitatory and inhibitory pulse coupling is considered, we found that synchronized dynamics becomes more difficult to achieve in the sense that the parameter regions where the synchronous state is stable are smaller. Numerical simulations of the coupled system are presented to validate these results. The stability of a network of coupled HH neurons is then analyzed and the stability regions in the parameter space are exactly obtained.

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Phys. Rev. E 71, 061904– Published 9 June, 2005
  • Received 3 January 2005

© 2005 American Physical Society

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