The authors investigate the dynamics of a system of two coupled oscillators, each of which has a separatrix loop in its uncoupled phase portrait. The effect of the coupling, which is of the diffusive viscous type, is to enhance the region Cε of phase space, which consists of all motions that do not escape to infinity. The authors offer numerically obtained descriptions of the region Cε, as well as some analytical investigations into its location and nature.
Magnus, W. and Winkler, S., 1966, Hill's Equation, Wiley , New York.
3.
Quinn, D.D. and Rand, R.H., 1995, "A perturbation approach to resonant capture," in Stability, Vibration and Control of Structures , A. Guran and D. Inman, eds., Prentice-Hall, Englewood Cliffs, NJ.
4.
Quinn, D., Rand, R., and Bridge, J., 1995, "The dynamics of resonant capture,"Nonlinear Dyncunics.
5.
Rand, R.H., 1994, Topics in Nonlinear Dynamics With Computer Algebra , Gordon & Breach, Langhorne, PA .
6.
Rand, R.H. and Armbruster, D., 1987, Perturbation Methods, Bifurcation Theory and Computer Algebra, Springer, New York .
7.
Rand, R.H. and Holmes, P.J., 1980, "Bifurcation of periodic motions in two weakly coupled van der Pol oscillators,"International Journal of Non-Linear Mechanics15, 387-399.
8.
Rand, R.H., Kinsey, R.J., and Mingori, D.L., 1992, "Dynamics of spinup through resonance,"International Journal of Nnn-Linear Mechanics27, 489-502.
9.
Rosenberg, R.M., 1966, "On nonlinear vibrations of systems with many degrees of freedom," in Advances in Applied Mechanics, Academic Press, New York, 155-242.
10.
Stoker, J.J., 1950, Nonlinear Vibrations in Mechanical and Electrical Systems , Wiley, New York.
11.
Vakakis, A.F., 1994, "Exponentially small splittings of manifolds in a rapidly forced duffing system,"Journal of Sound and Vibration170, 119-129.
