Resonance Tongues in Hill's Equations: A Geometric Approach
نویسندگان
چکیده
منابع مشابه
The geometry of resonance tongues: a singularity theory approach
Resonance tongues and their boundaries are studied for nondegenerate and (certain) degenerate Hopf bifurcations of maps using singularity theory methods of equivariant contact equivalence and universal unfoldings. We recover the standard theory of tongues (the nondegenerate case) in a straightforward way and we find certain surprises in the tongue boundary structure when degeneracies are presen...
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where ai(t) = Pi + εQi cos2t, where Pi,Qi and ε are given constants, and where it is assumed that when ε=0 this system exhibits a pair of linearly independent solutions of period 2π . Since the driver cos2t has period π , we have the ingredients for a 2:1 subharmonic resonance which typically results in a tongue of instability involving unbounded solutions when ε >0. We present conditions on th...
متن کاملGeometry of resonance tongues
Resonance tongues arise in bifurcations of discrete or continuous dynamical systems undergoing bifurcations of a fixed point or an equilibrium satisfying certain resonance conditions. They occur in several different contexts, depending, for example, on whether the dynamics is dissipative, conservative, or reversible. Generally, resonance tongues are domains in parameter space, with periodic dyn...
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Various resonant and near-resonant patterns form in a light-sensitive Belousov-Zhabotinsky (BZ) reaction in response to a spatially homogeneous time-periodic perturbation with light. The regions (tongues) in the forcing frequency and forcing amplitude parameter plane where resonant patterns form are identified through analysis of the temporal response of the patterns. Resonant and near-resonant...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2000
ISSN: 0022-0396
DOI: 10.1006/jdeq.2000.3804