A new theoretical model for the cross-bridge formation is proporsed, and the sliding motion of the many cross-bridge system is analysed by numerical simulations in reference to the Hill's relation of the muscle contraction. In the microscopic level of each cross-bridge dynamics, both chaotic and periodic oscillations are generated though the sliding motion is smooth. In the simulated Hill's relation, the periodic oscillasion is dominant in the micro-dynamics when the sliding speed is high, but the chaotic oscillation is generally induced in the regime with the low speed. Furthermore, the maximum efficiency in chemo-mechanical energy transformation is achieved in the transition regime from the periodic to the chaotic oscillation in micro-dynamics.
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