A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators |
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Institution: | 1. Departamento de Física, Universidade Federal do Paraná, 81531-990, PR, Brazil;2. Aix-Marseille Université CNRS, PIIM UMR 7345, 13397, Marseille, France Marseille Cedex 20, France |
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Abstract: | Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specifically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size. |
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