On the appearance of horseshoe chaos in a nonlinear hysteretic systems with negative stiffness

The problem of inhibition of horseshoe chaos in a nonlinear hysteretic systems using negative stiffness is investigated in this paper. The Bouc–Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. The analytical investigation of the Hamiltonian shows that the appearance of separatrix in the system is directly related to the parameters of the hysteretic forces. This means that the transverse intersection between the perturbed and unperturbed separatrix can be controlled according to the shape parameters of the hysteretic model.

Hysteretic Behavior in Voltage-Gated Channels

An ever-growing body of evidence has shown that voltage-gated ion channels are likely molecular systems that display hysteresis in their activity. This phenomenon manifests in the form of dynamic changes in both their voltage dependence of activity and their deactivation kinetics. The goal of this review is to provide a clear definition of hysteresis in terms of the behavior of voltage-gated channels. This review will discuss the basic behavior of voltage-gated channel activity and how they make these proteins into systems displaying hysteresis. It will also provide a perspective on putative mechanisms underlying hysteresis and explain its potential physiological relevance. It is uncertain whether all channels display hysteresis in their behavior. However, the suggested notion that ion channels are hysteretic systems directly collides with the well-accepted notion that ion channel activity is stochastic. This is because hysteretic systems are regarded to have “memory” of previous events while stochastic processes are regarded as “memoryless.” This review will address this apparent contradiction, providing arguments for the existence of processes that can be simultaneously hysteretic and stochastic.

A nonlinear observer-based adaptive robust control approach for a class of uncertain asymmetric hysteretic systems

This article presents a robust control scheme for a class of asymmetric hysteretic systems with both parametric uncertainties and external disturbances, where an asymmetric Bouc–Wen model is adopted to represent the hysteretic behavior. A novel adaptive non-singular terminal sliding mode control methodology with hysteretic state estimation is proposed to achieve finite-time stabilization of such systems for vibration suppressions. In the proposed control framework, a hysteresis observer is constructed to capture the unmeasurable hysteretic force, and the adaptive control technique is used to accommodate the hysteretic uncertainties and unknown system parameters. Moreover, a fast terminal sliding mode controller without the singularity problem is designed to improve the robustness and dynamic performance of such systems, where the terminal sliding mode function is proposed to guarantee the finite-time convergence of the system states, and the reaching law with fractional power is constructed to accelerate the occurrence of the corresponding terminal sliding mode surface. Meanwhile, the finite-time stability of the whole closed-loop system is also analyzed. Finally, numerical simulation results deployed on a magnetorheological elastomer vibration isolation system are provided to validate the effectiveness of the proposed control algorithm.