Wu Fuqiang, Wang Runxia
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China.
Chaos. 2019 Aug;29(8):083135. doi: 10.1063/1.5109752.
In this paper, we study the dynamics of an autonomous system for a hair bundle subject to mechanical load. We demonstrated the spontaneous oscillations that arise owing to interactions between the linear stiffness and the adapting stiffness. It is found that by varying the linear stiffness, the system can induce a weakly chaotic attractor in a certain region where the stable periodic orbit is infinitely close to a parabolic curve composed of unstable equilibrium points. By altering the adapting stiffness associated with the calcium concentration, the system is able to trigger the transition from the bistable resting state, through a pair of symmetric Hopf bifurcation, into the bistable limit cycle, even to the chaotic attractor. At a negative adapting stiffness, the system exhibits a double-scroll chaotic attractor. According to the method of qualitative theory of fast-slow decomposition, the trajectory of a double-scroll chaotic attractor in the whole system depends upon the symmetric fold/fold bifurcation in a fast system. Furthermore, the control of the adapting stiffness in the improved system with two slow variables can trigger a new transition from the bistable resting state into the chaotic attractor, even to the hyperchaotic attractor by observing the Lyapunov exponent.
在本文中，我们研究了受机械负载作用的毛细胞束自主系统的动力学特性。我们展示了由于线性刚度和适应性刚度之间的相互作用而产生的自发振荡。研究发现，通过改变线性刚度，系统能够在稳定周期轨道无限接近于由不稳定平衡点组成的抛物线的特定区域内诱导出一个弱混沌吸引子。通过改变与钙浓度相关的适应性刚度，系统能够通过一对对称的霍普夫分岔，触发从双稳静息状态到双稳极限环，甚至到混沌吸引子的转变。在负适应性刚度下，系统呈现出双涡卷混沌吸引子。根据快-慢分解定性理论的方法，整个系统中双涡卷混沌吸引子的轨迹取决于一个快速系统中的对称折叠/折叠分岔。此外，在具有两个慢变量的改进系统中，通过观察李雅普诺夫指数，对适应性刚度的控制能够触发从双稳静息状态到混沌吸引子，甚至到超混沌吸引子的新转变。
