Emergence of Chaotic Oscillation in a Mathematical Model for Contractile System of Muscle

In order to understand various properties of self-oscillation in a contractile system of muscle, we propose a mathematical inertial model (iModel) in the framework of nonlinear dynamics. This is a straightforward extension of the previously presented model in the absence of the contribution of effective inertia which is usually negligibly small in the lateral dynamics for spontaneous oscillatory contraction. We numerically show that by introducing the effective inertia of sarcomere, a small ripple component is superimposed on each sawtooth waveform in the slow contraction and fast relaxation of sarcomeres in myofibrils, which is distinct from the fluctuations and noises of chemical concentration, temperature, etc. Additionally, by use of iModel, we find numerically a chaotic oscillation with many ripple components superimposed on each sawtooth waveform for self-oscillation. We expect that iModel plays an important role in experimentally finding new patterns for self-oscillation with ripple components due to the effective inertia in the complex contractile systems.