Dynamics of four coupled phase-only oscillators. (English) Zbl 1122.70015

Summary: We study the dynamics of a system of four coupled phase-only oscillators. This system is analyzed using phase difference variables in a phase space that has the topology of three-dimensional torus. The system is shown to exhibit numerous phase-locked motions. The qualitative dynamics are shown to depend upon a parameter representing coupling strength. This work has application to MEMS artificial intelligence decision-making devices.


70K05 Phase plane analysis, limit cycles for nonlinear problems in mechanics
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
Full Text: DOI


[1] Aubin, K.; Zalalutdinov, M.; Alan, T.; Reichenbach, R.B.; Rand, R.; Zehnder, A., Limit cycle oscillations in CW laser-driven NEMS, J microelectromech syst, 13, 1018-1026, (2004)
[2] Hoppensteadt, F.; Izhikevich, E., Oscillatory neurocomputers with dynamic connectivity, Phys rev lett, 82, 2983-2986, (1999)
[3] Pandey M, Rand R, Zehnder A. Perturbation analysis of entrainment in a micromechanical limit cycle oscillator to appear. Comm Nonlinear Sci Numer Simulat, in press, doi:10.1016/j.cnsns.2006.01.017. · Zbl 1124.34026
[4] Paullet, J.E.; Ermentrout, G.B., Stable rotating waves in two-dimensional discrete active media, SIAM J appl math, 54, 1720-1744, (1994) · Zbl 0832.92002
[5] Rand RH. Lecture notes on nonlinear vibrations (version 52), available from: http://www.tam.cornell.edu/randdocs 2005.
[6] Rand, R.H.; Holmes, P.J., Bifurcation of periodic motions in two weakly coupled van der Pol oscillators, Int J nonlinear mech, 15, 387-399, (1980) · Zbl 0447.70028
[7] 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.