Computing Arnol′d tongue scenarios: some recent advances
نویسنده
چکیده
Many interesting models in science and engineering involve forced or coupled oscillators. The most striking feature of such systems is the transition between phase locking and quasi-periodicity. Phase locking produces a periodic solution that generically persists under variation of parameters. In contrast, quasi-periodicity is a codimension-one phenomenon, which is thus generically destroyed by perturbation. The manifestation of this transition is a well-known bifurcation diagram called the ‘Arnol′d tongue’ scenario. In this talk we present methods for computing Arnol′d tongue scenarios for maps and ordinary differential equations.
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