Total fractional-order variation regularization based image reconstruction method for capacitively coupled electrical resistance tomography

Compared with electrical resistance tomography, capacitively coupled electrical resistance tomography (CCERT) is preferred since it avoids problems of electrode corrosion and electrode polarization. However, reconstruction of conductivity distribution is still a great challenge for CCERT. To improve reconstruction quality, this work proposes a novel image reconstruction method based on total fractional-order variation regularization. Simulation work is conducted and reconstruction of several typical models is studied. Robustness of the proposed method to noise is also conducted. Additionally, the performance of the proposed reconstruction method is quantitatively evaluated. We have also carried out phantom experiment to further verify the effectiveness of the proposed method. The results demonstrate that the quality of reconstruction has been largely improved when compared with the images reconstructed by Landweber, Newton-Raphson and Tikhonov methods. The inclusion is more accurately reconstructed and the background is much clearer even under the impact of noise.     

New Fuzzy Fractional Epidemic Model Involving Death Population

In this research, we propose a new change in classical epidemic models by including the change in the rate of death in the overall population. The existing models like Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) include the death rate as one of the parameters to estimate the change in susceptible, infected and recovered populations. Actually, because of the deficiencies in immunity, even the ordinary flu could cause death. If people’s disease resistance is strong, then serious diseases may not result in mortalities. The classical model always assumes a closed system where there is no new birth or death, no immigration or emigration, while in reality, such assumptions are not realistic. Moreover, the classical epidemic model does not report the change in population due to death caused by a disease. With this study, we try to incorporate the rate of change in the population of death caused by a disease, where the model is framed to reduce the curve of death along with the susceptible and infected populations. Since the rate of change turned out to be very small, we have tried to estimate it fractionally. Thus, the model is defined using fuzzy logic and is solved by two different methods: a Laplace Adomian decomposition method (LADM) and a differential transform method (DTM) for an arbitrary order α. To test its accuracy, we compared the results of both DTM and LADM with the fourth-order Runge-Kutta method (RKM-4) at α = 1.     

Image encryption using linear weighted fractional-order transform

As the linear weighted fractional-order Fourier transform (LWFRFT), an extension of the Fourier transform, has been widely studied, many linear weighted fractional-order transforms (LWFRTs) have been proposed consequently. Our research shows that the LWFRT has limitations when applied to image encryption. For example, its application to image encryption leads to the security risks of key invalidation. In this paper, we propose a new reformulation of the LWFRT which establishes the relation between many fractional-order transforms. With the help of the new reformulation, we point out the limitations of the LWFRT and analyze the reasons for key invalidation in image encryption. Finally, numerical simulation verifies our perspective.     

New state-space approach and its application in thermoelasticity

In this work, a new state-space approach in the context of fractional-order theory of thermoelasticity is introduced. This new method utilizes the diagonalization of a square matrix by the use of its eigenvalues and vectors. This new approach is applied to a 1-D problem for a half-space subjected to a thermal shock. Laplace transform technique is used throughout. The inversion of the transforms is performed using a numerical inversion technique based on the Fourier series expansion technique. The effects of the time and the fractional parameter on variable field distributions are discussed and represented graphically.     

Intelligent fuzzy controller for chaos synchronization of uncertain fractional-order chaotic systems with input nonlinearities

In this research work, a novel fuzzy adaptive control is proposed to achieve a projective synchronization for a class of fractional-order chaotic systems with input nonlinearities (dead-zone together with sector nonlinearities). These master-slave systems under consideration are supposed to be with distinct models, different fractional-orders, unknown models, and dynamic external disturbances. The proposed control law consists of two main terms, namely: a fuzzy adaptive control term for appropriately approximating the uncertainties and a fractional-order variable-structure control term for robustly dealing with these inherent input nonlinearities. A Lyapunov approach is used to derive the updated laws and to prove the stability of the closed-loop control system. At last, a set of computer simulation results is carried out to illustrate and further validate the theoretical findings.     

基于Melnikov方法的分数阶Duffing振子混沌阈值解析研究

研究了含有分数阶微分项的Duffing振子的分岔与混沌行为,利用等效刚度和等效阻尼的概念对分数阶微分项进行处理,将分数阶微分项等效成三角函数与指数函数的形式,用Melnikov方法分析了分数阶Duffing振子产生分岔与混沌的必要条件,得到了其解析结果.进行了解析解和数值解的比较,证明了解析结果的精确度,并通过仿真计算...     

一种分数阶忆阻器的Verilog-A模型及应用

近年来,科研人员为研究忆阻器的电气特性及其在电路中的应用,建立了多种整数阶忆阻器的Verilog-A模型,但分数阶忆阻器的Verilog-A模型还未见报道.文章提出了一种分数阶忆阻器的Verilog-A模型,对其相关特性进行了分析,总结了参数对忆阻器电气特性影响的规律,并将此模型应用于脉冲宽度调制(PWM)电路中,通过...     

基于分数阶陈氏混沌系统的图像加密算法

由于分数阶混沌动力学系统比整数阶系统具有更复杂的动力学特性,且能为图像加密方案提供更多的自由度,基于分数阶陈氏混沌系统,提出了一种图像加密方法。在发送端,驱动系统产生混沌信号,利用混沌信号扰乱明文图像的像素位置,将扰乱后的图像掩盖在混沌信号中,得到传输的密文图像。在接收端,通过同步系统去掩盖,进行像素位置扰乱的逆操作,恢复明文图像。最后对提出的加密算法进行了安全性分析。实验结果表明,该加密算法安全性高,具有良好的研究价值和应用前景     

Observer-based quasi-containment of fractional-order multi-agent systems via event-triggered strategy

This paper is devoted to the quasi-containment control problem of fractional-order multi-agent systems (FOMASs). First, to reduce the frequency of communications, a novel observer-based event-triggered control mechanism which only relies on the information at the trigger-time is proposed. And then, by applying the theory of algebraic graph, matrix and fractional-order calculus, some sufficient consensus conditions based on the linear matrix inequality are established for achieving the consensus of FOMASs. In addition, the strict positive lower bound on the inter-event interval is obtained, which implies that the system is free from the Zeno behaviour. Finally, several simulation examples are presented to demonstrate the effectiveness of the theoretical results.     

Generalised exponential consensus of the fractional-order nonlinear multi-agent systems via event-triggered control

In this paper, the leader-following consensus problem of the fractional-order nonlinear multi-agent systems via event-triggered control is considered. An effective event-triggered controller is designed and then generalised exponential consensus of the controlled multi-agent systems is studied in the sense of Mittag-Leffler stability of fractional-order systems. The event-triggering function design is dependent on the parameter of the system structure and the minimum inter-event interval can be flexibly adjusted with different fractional-order α. With the event-triggered control scheme, the consensus condition is obtained and the convergence rate of the system is estimated. Numerical simulation indicates the effectiveness of the theoretical results.