Amplitude modulation control of spatiotemporal chaos in starlike networks of damped-driven pendula. (English) Zbl 1536.70027
Summary: Applying amplitude modulations to a parametrically excited damped pendulum is shown to be a reliable method to control (suppress or enhance) its chaotic behaviour. Analytical (Melnikov analysis) and numerical (Lyapunov exponents and bifurcation diagrams) results show an effective control scenario for a wide range of resonances between the two excitations implicated. Different routes of regularization as the chaos-controlling parameters vary are identified, including period-doubling and crises. The method’s effectiveness at suppressing spatiotemporal chaos of starlike networks of sinusoidally coupled chaotic pendula is demonstrated where effective regularization is obtained under localized control on an increasing number of pendula.
MSC:
| 70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |
| 70K28 | Parametric resonances for nonlinear problems in mechanics |
| 70Q05 | Control of mechanical systems |
Keywords:
parametrical excitation; sinusoidal coupling; Melnikov analysis; Lyapunov exponent; bifurcation diagram; period-doubling route to chaos; effective regularizationReferences:
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