Newhouse sinks in the self-similar bifurcation structure

The numerical analyses of the dynamics of periodically driven Toda oscillat or suggest the following features. Primary Newhouse orbits (sinks and saddl es) are born in sequence when the oscillator proceeds through various subha rmonic resonance regions. As the control parameter is swept in the neighbor ing parameter space of the homoclinic tangency for a primary saddle, first order secondary Newhouse sinks are born around the corresponding primary si nk in a series of period n-tupling (n>2) processes. Higher order secondary Newhouse sinks are similarly born, in a recurrent manner, around those firs t-order secondary sinks, constituting a self-similar bifurcation structure in the parameter space, Each higher (say nth) order secondary Newhouse sink appears and undergoes sequence of period doubling (before being destroyed by crises), within a small subinterval of the control parameter window wher e the (n-1)th-order secondary Neu house sink exists. The nth-order secondar y Newhouse orbits appear in the basin of the (n - 1)th-order secondary Newh ouse sink. Thus, the higher-order secondary sinks appear with progressively smaller basins intertwined with the basins of lower-order secondary sinks.