Mendelowitz, Lee; Verdugo, Anael; Rand, Richard Dynamics of three coupled limit cycle oscillators with application to artificial intelligence. (English) Zbl 1221.34099 Commun. Nonlinear Sci. Numer. Simul. 14, No. 1, 270-283 (2009). Summary: We study a system of three limit cycle oscillators which exhibits two stable steady states. The system is modeled by both phase-only oscillators and by van der Pol oscillators. We obtain and compare the existence, stability and bifurcation of the steady states in these two models. This work is motivated by application to the design of a machine which can make decisions by identifying a given initial condition with its associated steady state. Cited in 9 Documents MSC: 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations Keywords:MEMS oscillators; associative memory; phase-locked motion; coupled oscillators PDFBibTeX XMLCite \textit{L. Mendelowitz} et al., Commun. Nonlinear Sci. Numer. Simul. 14, No. 1, 270--283 (2009; Zbl 1221.34099) Full Text: DOI References: [1] Hoppensteadt, F.; Izhikevich, E., Oscillatory neurocomputers with dynamic connectivity, Phys Rev Lett, 82, 2983-2986 (1999) [2] Zalalutdinov, M. K.; Baldwin, J. W.; Marcus, M. H.; Reichenbach, R. B.; Parpia, J. M.; Houston, B. H., Two-dimensional array of coupled nanomechanical resonators, Appl Phys Lett, 88, 143504 (2006) [3] Rand R, Wong J. Dynamics of four coupled phase-only oscillators. Commun Nonlinear Sci Numer Simul. doi:10.1016/j.cnsns.2006.06.013; Rand R, Wong J. Dynamics of four coupled phase-only oscillators. Commun Nonlinear Sci Numer Simul. doi:10.1016/j.cnsns.2006.06.013 · Zbl 1122.70015 [4] Cohen, A. H.; Holmes, P. J.; Rand, R. H., The nature of the coupling between segmental oscillators of the lamprey spinal generator for locomotion: a mathematical model, J Math Biol, 13, 345-369 (1982) · Zbl 0476.92003 [5] Kuramoto, Y., Chemical oscillations, waves and turbulence (2003), Dover · Zbl 0558.76051 [6] Nishiyama, N.; Eto, K., Experimental study on three chemical oscillators coupled with time delay, J Chem Phys, 100, 6977-6978 (1994) [7] Ashwin, P.; King, G. P.; Swift, J. W., Three identical oscillators with symmetric coupling, Nonlinearity, 3, 585-601 (1990) · Zbl 0708.58020 [8] Cole, J. D., Perturbation methods in applied mathematics (1968), Blaisdell Pub. Co. · Zbl 0162.12602 [9] Nayfeh, A. H., Perturbation methods (1973), Wiley [10] Rand RH. Lecture notes on nonlinear vibrations (version 52). Available from: 〈;http://audiophile.tam.cornell.edu/randdocs/nlvibe52.pdf⟩; Rand RH. Lecture notes on nonlinear vibrations (version 52). Available from: 〈;http://audiophile.tam.cornell.edu/randdocs/nlvibe52.pdf⟩ [11] Rompala, K.; Rand, R.; Howland, H., Dynamics of three coupled van der Pol oscillators with application to circadian rhythms, Commun Nonlinear Sci Numer Simulat, 12, 794-803 (2007) · Zbl 1120.34025 [12] Strogatz, S. H., Nonlinear dynamics and chaos (1994), Addison-Wesley 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.