Pogromsky, Alexander; Glad, Torkel; Nijmeijer, Henk On diffusion driven oscillations in coupled dynamical systems. (English) Zbl 0970.34029 Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 4, 629-644 (1999). Summary: The authors deal with the problem of destabilization of diffusively coupled identical systems. Following a question of S. Smale [J. Math. Biol. 3, 5-7 (1976; Zbl 0344.92009)], it is shown that globally asymptotically stable systems being diffusively coupled, may exhibit oscillatory behavior. It is shown that if the diffusive medium consists of hyperbolically nonminimum phase systems and the diffusive factors exceed some threshold value, the origin of the overall system undergoes a Poincaré-Andronov-Hopf bifurcation resulting in oscillatory behavior. Cited in 33 Documents MSC: 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 93C10 Nonlinear systems in control theory 34C23 Bifurcation theory for ordinary differential equations 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 34H05 Control problems involving ordinary differential equations Keywords:diffusion driven oscillations; destabilization; diffusively coupled identical systems; Poincaré-Andronov-Hopf bifurcation Citations:Zbl 0344.92009 PDFBibTeX XMLCite \textit{A. Pogromsky} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, No. 4, 629--644 (1999; Zbl 0970.34029) Full Text: DOI References: [1] DOI: 10.1109/9.90226 · Zbl 0758.93060 · doi:10.1109/9.90226 [2] DOI: 10.1109/9.100932 · Zbl 0758.93007 · doi:10.1109/9.100932 [3] Kocarev L. M., IEEE Trans. Circuits Syst. (1995) [4] DOI: 10.2307/1969299 · Zbl 0061.18910 · doi:10.2307/1969299 [5] DOI: 10.1142/S0218127498000188 · Zbl 0938.93056 · doi:10.1142/S0218127498000188 [6] DOI: 10.1137/0109053 · Zbl 0108.01202 · doi:10.1137/0109053 [7] Tomberg E. A., Siberian Math. J. 30 (4) pp 180– (1989) [8] DOI: 10.1098/rstb.1952.0012 · Zbl 1403.92034 · doi:10.1098/rstb.1952.0012 [9] We M., Notices of the Am. Math. Soc. 45 (1) pp 9– (1998) [10] Yakubovich V. A., Siberian Math. J. 14 (5) pp 1100– (1973) [11] DOI: 10.1007/BF00276172 · Zbl 0096.28902 · doi:10.1007/BF00276172 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.