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Description
Spontaneous oscillations are observed across many natural and artificial systems. We present a comparative analysis of the chemo-mechanical mechanisms that drive spontaneous oscillations in two distinct active filamentous structures: photo-chemically deformable liquid crystal elastomer (LCE) rods and ATP-powered eukaryotic cilia.
Using the unifying framework of active planar rods, we develop simplified mathematical models for both systems. We reduce the governing partial differential equations to one-degree-of-freedom (1-DOF) nonlinear oscillators, each undergoing a supercritical Hopf bifurcation. For these reduced models, we obtain explicit analytical expressions for the onset and characteristics of self-sustained oscillations.
Despite the common mathematical structure, the underlying physical mechanisms are fundamentally different. For LCEs, self-oscillation is an inertial phenomenon driven by an elastic-inertial feedback over the timescale of the photochemical reaction. In contrast, eukaryotic cilia live in the inertia-less (low Reynolds number) regime, and the instability is driven by a negative effective damping - a motive force that arises from the mechano-chemistry of molecular motors. The analytical predictions for critical activation thresholds, frequencies, and amplitudes agree with full nonlinear simulations, providing quantitative insight into the dynamics of these complex self-oscillating systems.