Transition between multimode oscillations in a loaded hairbundle

In this paper, we study the dynamics of an autonomous system for a hair bundle subject tomechanical load. We demonstrated the spontaneous oscillations that arise owing tointeractions between the linear stiffness and the adapting stiffness. It is found that byvarying the linear stiffness, the system can induce a weakly chaotic attractor in acertain region where the stable periodic orbit is infinitely close to a parabolic curvecomposed of unstable equilibrium points. By altering the adapting stiffness associatedwith the calcium concentration, the system is able to trigger the transition from thebistable resting state, through a pair of symmetric Hopf bifurcation, into the bistablelimit cycle, even to the chaotic attractor. At a negative adapting stiffness, the systemexhibits a double-scroll chaotic attractor. According to the method of qualitative theoryof fast-slow decomposition, the trajectory of a double-scroll chaotic attractor in thewhole 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 slowvariables can trigger a new transition from the bistable resting state into the chaoticattractor, even to the hyperchaotic attractor by observing the Lyapunov exponent.At the request of the authors, this article is being retracted effective 13 April 2020.