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This article introduces the global exponential multi switching combination synchronization (GEMSCS) for three different chaotic systems with known parameters in the master-slave system configuration. The proposed GEMSCS scheme establishes the global exponential stability of the synchronization error at the origin with different combinations of state variables of the two master chaotic systems with the state variables of a slave chaotic system in diverse manners. Consequently, it increases the complexity level of the information signal in secure communications. To study the GEMSCS, an efficient nonlinear control algorithm is designed. The Lyapunov direct theorem is used to accomplish the global exponential stability of the synchronization error at the origin. The stability conditions are derived analytically. To show the effectiveness and advantages of the proposed GEMSCS control approach, two numerical examples are presented. The computer based simulation results are compared with the reported works in the relevant literature. This article also extends the idea of GEMSCS to the secure communication using the chaotic masking technique. Using the GEMSCS strategy, the information signal is recovered at the receiving system with good accuracy and high speed while the parameters of the transmitter and receiver systems mismatch. At the end, some future research problems related to this work are suggested.

In this paper, an adaptive control scheme is developed to study the dual anti-synchronization behavior between two chaotic systems with fully uncertain parameters. This adaptive anti-synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. The adaptive dual anti-synchronization between two chaotic systems are taken to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are shown to verify the results.

The adaptive dual synchronization problem of chaotic and hyperchaotic systems with fully uncertain parameters is addressed in this paper. The sufficient conditions for achieving the dual synchronization of two chaotic and hyperchaotic systems are derived based on Lyapunov stability theory. An adaptive controller associated with the parameters update rule is developed to make the states of two chaotic and hyperchaotic systems asymptotically dual synchronized. Theoretical analysis and numerical simulations are shown to verify the results.

By using two scaling matrices, the synchronization problem of different dimensional fractional order chaotic systems in different dimensions is developed in this article. The controller is designed to assure that the synchronization of two different dimensional fractional order chaotic systems is achieved using the fractional-order Lyapunov direct method. Numerical examples and computer simulations are used to validate numerically the proposed synchronization schemes.

In this article, a novel robust nonlinear controller approach is focused to study theoretically, the reduced-order synchronization phenomena of two unrelated time-delayed chaotic systems under the determined and unknown parameters. It is assumed that the two systems are perturbed by the bounded unstructured uncertainties and unknown external disturbance. Based on the Lyapunov–Krasovskii functional theory, a robust nonlinear synchronization controller is focused and a suitable Lyapunov functional is constructed so that they establish the globally asymptotical stability of the closed-loop at the origin. Subsequently, suitable adaptive laws of unknown parameters are designed to identify the unknown parameters. Finally, the effectiveness of the proposed reduced-order synchronization approach is verified by numerical simulations. A brief comparison of the present study with prior works has been given.

The epitome of this paper centers on chaos synchronization problem of different dimensional chaotic systems in different dimensions using two scaling matrices, the Lyapunov stability theory, and the stability theory of linear system. The controller is designed to assure that the synchronization of two different dimensional chaotic systems is achieved. Numerical examples and computer simulations are used to validate, numerically, the proposed synchronization schemes.

Structure, electrical resistivity, hardness, elastic modulus and roughness of Sn–10%Sb–2%Cu–x%Zn [x = 0.5, 1.0, 1.5, 2.0, 2.5 wt.%] rapidly solidified alloys have been investigated. Investigations have been made by using X-ray diffraction, scanning electron microscope (SEM), double bridge, Vickers hardness tester, the dynamic resonance technique and surface roughness tester. X-ray diffraction showed that, adding different amounts of zinc to the Sn–10%Sb–2%Cu changed its structural properties which affect all measured physical properties. Elastic modulus, hardness and electrical resistivity are increased by increasing the zinc content. Internal friction and roughness are varied. According to our results, the Sn–10%Sb–2%Cu–2.5%Zn alloy has good properties for bearing applications.

In this paper, we demonstrate that anti-synchronization can coexist in two different hyperchaotic systems with terms of parametric uncertainty and external disturbances using the robust active sliding mode control method. By using rigorous mathematical theory, the sufficient condition is drawn for the stability of error dynamics based on the Lyapunov stability theory, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis.

In this paper, we investigate the reduced-order anti-synchronization of uncertain chaotic systems. Based upon the parameters modulation and the adaptive control techniques, we show that dynamical evolution of third-order chaotic system can be anti-synchronized with the canonical projection of a fourth-order chaotic system even though their parameters are unknown. The techniques are successfully applied to two examples: hyperchaotic Lorenz system (fourth-order) and Lorenz system (third-order); Lu hyperchaotic system (fourth-order) and Chen system (third-order). Theoretical analysis and numerical simulations are shown to verify the results.

Creep behavior of Sn–Sb based quaternary alloys have been investigated by indentation method at room temperature. Stress exponent values have been determined using Mulheam–Tabor method and the calculated exponents are in good agreement with the values of Sn based reported in the literature. The stress exponent values in the range of 3.39–5.12. Elastic modulus and internal friction of Sn–Sb based alloys have been studied and analyzed.

This paper brings attention to hyperchaos anti-synchronization between two identical and different hyperchaotic systems by using adaptive control. The sufficient conditions for achieving the anti-synchronization of two hyperchaotic systems are derived based on Lyapunov stability theory. An adaptive control law and a parameter update rule for unknown parameters are introduced such that the hyperchaotic Chen system is controlled to be the hyperchaotic Lu system. Theoretical analysis and numerical simulations are shown to verify the results.

The epitome of this paper centers on the application of the differential transformation method (DTM) the renowned Chen system which is described as a three-dimensional system of ODEs with quadratic nonlinearities. Numerical comparisons are made between the DTM and the classical fourth-order Runge–Kutta method (RK4). Our work showcases the precision of the DTM as the Chen system transforms from a non-chaotic system to a chaotic one. Since the Lyapunov exponent for this system is much higher compared to other chaotic systems, we shall highlight the difficulties of the simulations with respect to its accuracy. We wrap up our investigations to reveal that this direct symbolic–numeric scheme is effective and accurate.

Based on the nonlinear control and Lyapunov stability theory, the anti-synchronization between two identical and different chaotic systems is investigated, where the antisynchronization can be characterized by the vanishing of the sum of relevant variables in chaotic systems, such that the Lu system is controlled to be the Lorenz system. Theoretical analysis and numerical simulations are shown to verify the results.

In this Letter, an adaptive control scheme is developed to study the anti-synchronization behavior between two identical and different chaotic systems with unknown parameters. This adaptive anti-synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. The adaptive anti-synchronization between two identical systems (Chen system) and different systems (Genesio and Lu systems) are taken as two illustrative examples to show the effectiveness of the proposed method. Theoretical analysis and numerical simulations are shown to verify the results.

Based on the nonlinear control theory, the anti-synchronization between two different hyperchaotic systems is investigated. Through rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical simulations are performed for the hyperchaotic Chen system and the hyperchaotic Lu system to demonstrate the effectiveness of the proposed control strategy.

The aim of this paper is to investigate the accuracy of the Adomian decomposition method for solving the hyperchaotic Rossler system, which is a four-dimensional system of ODEs with quadratic nonlinearities. Comparisons between the decomposition solutions and the fourth-order Runge–Kutta (RK4) solutions are made. It is found that the comparable accuracy of the ADM with the RK4 for the chaotic Lorenz system does not carry to the hyperchaotic Rossler system.

The aim of this paper is to investigate the accuracy of the differential transformation method (DTM) for solving the hyperchaotic Rossler system, which is a four-dimensional system of ODEs with quadratic nonlinearities. Comparisons between the DTM solutions and the fourth-order Runge–Kutta (RK4) solutions are made. The DTM scheme obtained from the DTM yields an analytical solution in the form of a rapidly convergent series. The direct symbolic-numeric scheme is shown to be efficient and accurate.

Renal transplantation has become an effective form of treatment for end-stage renal failure. Unfortunately, as a consequence of immunological and nonimmunological pathogenic mechanisms, chronic allograft nephropathy is responsible for the loss of a large proportion of kidney grafts after several years and return to dialysis. We have reported herein our 24 years of experience with second kidney transplantations. Of 1,302 kidney transplantations between January 1983 and June 2007 performed in our transplantation center, 100 were second transplantations. Kidney retransplantation was performed in 74 men and 26 women of overall mean age of 35.4 +/- 12.6 years. Cadaveric donor grafts were transplanted in 92 patients, whereas the remaining 8 were living-related donor kidneys. At 1, 5, and 10 years after kidney transplantation, patient survival rates were 100%, 96%, and 92%, respectively, whereas graft survival rates were 85%, 72%, and 53%, respectively. Immunosuppressive therapy included induction therapy with polyclonal anti-lymphocyte antibodies (ALG/ATG) or (starting from 1999) monoclonal anti CD 25 antibody. Our results demonstrated good outcomes for kidney retransplantations with allocation based on anti- HLA antibody identification together with induction immunosuppression.

Objectives: To evaluate the effects of introducing routine ultrasonic screening for the identification and elective surgical treatment of abdominal aortic aneurysms (AAA) at high risk of rupture in the U.K. population of men aged 65–74 years. Design: A computer assisted simulation of an AAA screening programme. The simulation incorporated assumptions gleaned from the literature about the epidemiology of AAA and the costs of screening. In addition, up to date costings based on recent Manchester (U.K.) vascular surgery experience are used. Setting: A dialogue between National Health Service commissioners and providers to explore the feasibility and desirability of introducing AAA screening. Chief outcome measure: Cost per quality adjusted life year (QALY) gained. Main results: The absolute cost (circa 1992/3) per QALY gained from screening for and treating aneurysms of ≥ 6cm in diameter is £1500 (benefit not discounted). Offsetting current treatment costs of ruptured aneurysms gives a net additional cost per QALY of £1300. Screening and treating aneurysms of ≥ 5cm leads to a cost per QALY gained exceeding £20000. The findings are robust under sensitivity analysis. Conclusions: Routine screening for AAAs of size ≥ 6cm compares favourably in terms of cost per QALY gained with services such as breast and cervical cancer screening.