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Mechanism of long transient oscillations in cyclic coupled systems

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  • Kitajima, Hiroyuki
  • Horikawa, Yo

Abstract

We consider unidirectionally coupled ring networks of neurons with inhibitory connections. It is known that when a number of inhibitory neurons is even, the system never has stable oscillatory modes. However, we observed oscillatory modes in such a case. In this paper, we clarify the oscillation mechanism in a state space. We investigate the relationship between these oscillatory modes and the unstable periodic solutions (UPSs) generated by the Hopf bifurcations. As a result we find that these transient oscillatory modes are generated by trajectories closing to the UPS and staying around it for a long time. We also confirm this phenomenon in a simple electrical circuit using inverting operational amplifiers.

Suggested Citation

  • Kitajima, Hiroyuki & Horikawa, Yo, 2009. "Mechanism of long transient oscillations in cyclic coupled systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1854-1859.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1854-1859
    DOI: 10.1016/j.chaos.2009.03.103
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    References listed on IDEAS

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    1. Kazuki Horikawa & Kana Ishimatsu & Eiichi Yoshimoto & Shigeru Kondo & Hiroyuki Takeda, 2006. "Noise-resistant and synchronized oscillation of the segmentation clock," Nature, Nature, vol. 441(7094), pages 719-723, June.
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