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

Rand, Richard; Wong, Jeffrey

Commun. Nonlinear Sci. Numer. Simul. 13, No. 3, 501-507 (2008).

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.

MSC:

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

Keywords:

nonisolated equilibria; phase-locked motion; phase space

References:

[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