Mechanism of long transient oscillations in cyclic coupled systems

Hiroyuki Kitajima and Yo Horikawa

Chaos, Solitons & Fractals, 2009, vol. 42, issue 3, 1854-1859

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:42:y:2009:i:3:p:1854-1859

DOI: 10.1016/j.chaos.2009.03.103

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