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Limit Cycles Arising in a Chain of Inhibitorily Coupled Identical Relaxation Oscillators Near the Self-Oscillation Threshold

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Abstract

We consider the dynamic regimes arising in a linear chain of four identical stiff FitzHugh- Nagumo oscillators existing in the vicinity of the bifurcation of limit cycle emergence. It is shown that in a broad range of coupling forces, slow-variable exchange between the oscillators gives rise to multiple limit cycles with different periods and different phase relations. In addition to the expected antiphase solutions, three families of stable limit cycles that differ in the number of bursts of the fast variable in the neighboring elements and in the number of bursts per period are detected. The boundaries of attractor stability are calculated and the parameter regions of their coexistence are found.

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  1. P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia

    E. I. Volkov

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 3, pp. 238–248, March 2005.

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Volkov, E.I. Limit Cycles Arising in a Chain of Inhibitorily Coupled Identical Relaxation Oscillators Near the Self-Oscillation Threshold. Radiophys Quantum Electron 48, 212–221 (2005). https://doi.org/10.1007/s11141-005-0062-1

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  • DOI: https://doi.org/10.1007/s11141-005-0062-1

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