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It is known that a shunted nonlinear resistive-capacitive-inductance Josephson-junction (RCLSJ) model has a chaotic attractor. This attractor is created as a result of Hopf bifurcation that occurs when a certain direct current (DC) applied to one of the junction terminals. This chaotic attractor prevents the system from reaching the phase-locked state and hence degrade the performance of the junction. This paper aims at controlling and taming this chaotic attractor induced in this model and pulling the system to the phase-locked state. To achieve this task, a sliding mode controller is proposed. The design procedures involve two steps. In the first one, we construct a suitable sliding surface so that the dynamic of the system follows the sliding manifolds in order to meet design specifications. Secondly, a control law is created to force the chaotic attractor to slide on the sliding surface and hence stabilizes system trajectory. The RCLSJ model under consideration is simulated with and without the designed controller. Results demonstrate the validity of the designed controller in taming the induced chaos and stabilizing the system under investigation.

In this paper, the modern nonlinear theory is applied to a third order phase locked loop (PLL) with a feedback time delay. Due to this delay, different behaviors that are not accounted for in a conventional PLL model are identified, namely, oscillatory instability, periodic doubling and chaos. Firstly, a Pade approximation is used to model the time delay where it is utilized in deriving the state space representation of the PLL under investigation. The PLL under consideration is simulated with and without time delay. It is shown that for certain loop gain (control parameter) and time delay values, the system changes its stability and becomes chaotic. Simulations show that the PLL with time delay becomes chaotic for control parameter value less than the one without time delay, i.e, the stable region becomes narrower. Moreover, the chaotic region becomes wider as time delay increases.

The nonlinear dynamics of a third-order phase locked loop (PLL) reveals a chaotic behavior for range values of loop parameter. Using bifurcation theory, it has been verified through mathematical analysis and simulation that such behavior pulls the PLL to an undesirable and unstable out-of-lock state. This paper aims to control such chaotic behavior and drive the PLL to the in-lock state, by applying a nonlinear controller based on sliding mode control theory to the PLL under consideration. The design process involves two phases. In the first phase, a sliding surface is designed such that the sliding motion meets the design specifications. In the second phase, a high-speed switching control law is selected such that the system state trajectory reaches the sliding surface. The validity of the proposed controller is tested through simulations. Results show the effectiveness of the designed nonlinear controller in stabilizing the system and driving the PLL to the phase locked state.

Background The endothelin system (ES) plays an important role in blood pressure (BP) regulation and also in the pathophysiology of idiopathic dilated cardiomyopathy (DCM). Recently, we demonstrated that a genetic polymorphism in the endothelin A (ET A ) receptor gene was associated with survival in DCM patients. The aim of this study was to determine whether polymorphisms in the ET A receptor gene might be associated with the severity of DCM. Methods One hundred twenty-four consecutively recruited unrelated patients with DCM, who underwent a detailed phenotyping protocol, were genotyped for the ET A receptor G-231A polymorphism using a hybridization technique with allele-specific oligonucleotides. Results The exon 1 G-231A polymorphism of the ET A receptor gene, upstream of the translation start site, was significantly associated with directly measured intra-aortic pressure in that −231A allele carriers had significantly lower systolic ( P = .0043), as well as mean ( P = .0016) and diastolic ( P = .0041) aortic pressure compared to noncarriers. The association of ET A G-231A with aortic pressure was independent from other factors such as prior medication, left ventricular end-diastolic diameter, age, gender, and New York Heart Association (NYHA) functional classification. However, no such association was seen for cuff BP and survival rates were not significantly different between −231A allele carriers and −231G homozygotes (log rank test, P = .66). No significant association with any other parameter investigated in the present study could be observed, even when men and women were analyzed separately. Conclusions Our results suggest an association of genetic variation in the ET A receptor gene with aortic pressure in patients with DCM.