Nonlinear, Singular Oscillatory Systems

TL;DRAbstract

Abstract : Recently, a new class of nonlinear oscillatory equations have arisen. They have the property that the nonlinear terms can become unbounded for finite values of the variable and/or its derivative. For such systems the usual method of analysis do not apply. This report summarizes our investigations on such systems. In particular, we have carried out a detailed investigation of the mathematical properties of such systems using phase-space methods, perturbation theory based on the Hopf bifurcation theorem, and the method of harmonic balance. Properties of coupled singular oscillators were also examined.

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