Dynamics and routes to strange non-chaotic behaviour in MEMS resonators: analysis and characterisation

Abstract

The present study deals with the dynamics of microelectromechanical system (MEMS) resonators, especially the exploration of strange non-chaotic attractor (SNA) in MEMS resonators. SNAs often arise in systems driven by quasiperiodic forces, where the system is subjected to multiple frequencies that are incommensurate. When we apply the quasiperiodic forces, we identify the presence of SNA regions in the MEMS oscillators through bifurcation and Lyapunov analysis. Subsequently, we analyse the route of SNA in the considered system. In our analysis, the first identified route to SNA is the fractilisation route which is validated through various analyses, such as Poincaré map, distribution of finite-time Lyapunov exponents, Lyapunov variance, singular continuous spectrum and recurrence analysis. Moreover, two additional routes to SNA, namely Haegy–Heamel route and intermittency route, are identified and thoroughly investigated, and the presence of SNA is confirmed using singular continuous spectrum analysis. This work helps to understand SNA that can be important in fields like signal processing, where distinguishing between chaotic and non-chaotic signals is crucial. In particular, the emergence and characterisation of SNAs in MEMS resonators open avenues for further research and applications in nonlinear dynamics and chaotic systems.