Phase-locking in nonidentical coupled light-fueled liquid crystal elastomer self-oscillators

Self-oscillation refers to feedback-driven and sustained periodic motion without external periodic forcing. In practice, self-oscillators often exist as collectives of nonidentical units, whose intrinsic differences give rise to intricate dynamics of competition and compromise. A theoretical model of two nonidentical liquid crystal elastomer self-oscillators coupled by a spring is established. Each oscillator comprises a liquid crystal elastomer fiber and a mass block, displaying self-oscillation under a linear gradient optical field. The distinct frequencies of the two oscillators are achieved by varying the elastic coefficient of the liquid crystal elastomer fiber. Numerical simulations reveal both asynchronization and phase-locking synchronization, including in-phase and anti-phase locking. The underlying mechanisms are explored in the time domain, frequency domain, and phase space. The multiscale method is also utilized to derive the amplitude and phase difference equations, enabling a stability and bifurcation analysis. The Arnold tongue reveals the existence of both monostable and bistable phase-locking regimes. Transitions from asynchrony to phase locking, as well as between monostable and bistable regimes, are governed by the coupling strength and frequency detuning. Numerical and analytical results show close agreement on the effects of these two parameters on phase-locking behaviors. This theoretical framework lays the foundation for investigating the collective synchronization dynamics in large-scale networks of liquid crystal elastomer self-oscillators and opens new avenues for constructing liquid crystal elastomer-based logic gates by leveraging programmable synchronization modes.