Arnol’d tongues

Fig. 13.14. The excitation diagram for the Takoudis-Schmidt-Aris model showing resonance horns (Arnol d tongues) emerging from integer quotients of forcing and natural frequencies. For details of the behaviour in the closed broken curve see Fig. 13.16. (Reproduced with permission from McKarnin, M. A. et al. (1988). Proc. R. Soc., A417, 363-88.)...

Figure 32 Phase plane portrait showing Arnol d tongues, which come to a point on the A = 0 axis and widen out as K increases. Within the wedge-shaped regions, mode-locked states exist. Above = 1, these wedges overlap, leading to the possibility of chaos in this system. (Adapted from a similar figure in Ref. 75.)...

Figure 12.1 Arnol d tongue structure for a typical forced nonlinear oscillator.

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