A Poincare map based analysis of stroke patients' walking after a rehabilitation by a robot

A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.

Dynamics and Entropy Analysis for a New 4-D Hyperchaotic System with Coexisting Hidden Attractors

This paper presents a new no-equilibrium 4-D hyperchaotic multistable system with coexisting hidden attractors. One prominent feature is that by varying the system parameter or initial value, the system can generate several nonlinear complex attractors: periodic, quasiperiodic, multiple topology chaotic, and hyperchaotic. The dynamics and complexity of the proposed system were investigated through Lyapunov exponents (LEs), a bifurcation diagram, a Poincaré map, and spectral entropy (SE). The simulation and calculation results show that the proposed multistable system has very rich and complex hidden dynamic characteristics. Additionally, the circuit of the chaotic system is designed to verify the physical realizability of the system. This study provides new insights into uncovering the dynamic characteristics of the coexisting hidden attractors system and provides a new choice for nonlinear control or chaotic secure communication technology.

A Review on the Control of the Mechanical Properties of Ankle Foot Orthosis for Gait Assistance

In the past decade, advanced technologies in robotics have been explored to enhance the rehabilitation of post-stroke patients. Previous works have shown that gait assistance for post-stroke patients can be provided through the use of robotics technology in ancillary equipment, such as Ankle Foot Orthosis (AFO). An AFO is usually used to assist patients with spasticity or foot drop problems. There are several types of AFOs, depending on the flexibility of the joint, such as rigid, flexible rigid, and articulated AFOs. A rigid AFO has a fixed joint, and a flexible rigid AFO has a more flexible joint, while the articulated AFO has a freely rotating ankle joint, where the mechanical properties of the AFO are more controllable compared to the other two types of AFOs. This paper reviews the control of the mechanical properties of existing AFOs for gait assistance in post-stroke patients. Several aspects that affect the control of the mechanical properties of an AFO, such as the controller input, number of gait phases, controller output reference, and controller performance evaluation are discussed and compared. Thus, this paper will be of interest to AFO researchers or developers who would like to design their own AFOs with the most suitable mechanical properties based on their application. The controller input and the number of gait phases are discussed first. Then, the discussion moves forward to the methods of estimating the controller output reference, which is the main focus of this study. Based on the estimation method, the gait control strategies can be classified into subject-oriented estimations and phase-oriented estimations. Finally, suggestions for future studies are addressed, one of which is the application of the adaptive controller output reference to maximize the benefits of the AFO to users.