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In this work, a novel 6D four-wing hyperchaotic system with a line equilibrium based on a flux-controlled memristor model is proposed. The novel system is inspired from an existing 5D four-wing hyperchaotic system introduced by Zarei (2015). Fundamental properties of the novel system are discussed, and its complex behaviors are characterized using phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. When a suitable set of parameters are chosen, the system exhibits a rich repertoire of dynamic behaviors including double-period bifurcation of the quasiperiod, a single two-wing, and four-wing chaotic attractors. Further analysis of the novel system shows that the multiple coexisting attractors can be observed with different system parameter values and initial values. Moreover, the feasibility of the proposed mathematical model is also presented by using Multisim simulations based on an electronic analog of the model. Finally, the active control method is used to design the appropriate controller to realize the synchronization between the proposed 6D memristive hyperchaotic system and the 6D hyperchaotic Yang system with different structures. The Routh–Hurwitz criterion is used to prove the rationality of the controller, and the feasibility and effectiveness of the proposed synchronization method are proved by numerical simulations.

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This paper provides a unified method for analyzing chaos synchronization of the generalized Lorenz systems. The considered synchronization scheme consists of identical master and slave generalized Lorenz systems coupled by linear state error variables. A sufficient synchronization criterion for a general linear state error feedback controller is rigorously proven by means of linearization and Lyapunov's direct methods. When a simple linear controller is used in the scheme, some easily implemented algebraic synchronization conditions are derived based on the upper and lower bounds of the master chaotic system. These criteria are further optimized to improve their sharpness. The optimized criteria are then applied to four typical generalized Lorenz systems, i.e. the classical Lorenz system, the Chen system, the Lü system and a unified chaotic system, obtaining precise corresponding synchronization conditions. The advantages of the new criteria are revealed by analytically and numerically comparing their sharpness with that of the known criteria existing in the literature.

Although X-ray imaging has played a dominant role in cardiac catheter-based interventions, sometimes 3D soft tissue information, which X-ray images cannot provide, may be required. In contrast, 3D echocardiographic imaging is able to visualise soft tissue. In this paper, we propose a real-time catheter tracking strategy in echocardiographic sequences based on catheter tracking in 2D X-ray images and registration between these two modalities. The catheter tracking in X-ray images can be divided into catheter initialization and tracking. For initialization, an extraction algorithm based on SURF features, patch analysis and Kalman filtering is used to locate the catheter in the first X-ray image. Following this, a tracking algorithm based on patch analysis and Fast-PD optimization is used to track the catheter in the following images. The tracking result of each X-ray frame, as well as the transformation between X-ray and ultrasound images obtained from registration, is used to reduce the search space in the echo volume to only a curved surface. Using a graphical model and shortest path optimization, the position of the catheters in each echo frame can be estimated. Based on 10 pairs of X-ray and US sequences, comprising more than 800 frames, our experimental results show that the tracking system can track catheters with an average error of less than 1mm in X-ray images and less than 2mm in US. Also, our strategy for tracking in X-ray outperforms previous methods using only Fast-PD. The speed in total can reach 1.5 fps.

Novel memristive hyperchaotic system designs and their engineering applications have received considerable critical attention. In this paper, a novel multistable 5D memristive hyperchaotic system and its application are introduced. The interesting aspect of this chaotic system is that it has different types of coexisting attractors, chaos, hyperchaos, periods, and limit cycles. First, a novel 5D memristive hyperchaotic system is proposed by introducing a flux-controlled memristor with quadratic nonlinearity into an existing 4D four-wing chaotic system as a feedback term. Then, the phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy are used to analyze the basic dynamics of the 5D memristive hyperchaotic system. For a specific set of parameters, we find an unusual metastability, which shows the transition from chaotic to periodic (period-2 and period-3) dynamics. Moreover, its circuit implementation is also proposed. By using the chaoticity of the novel hyperchaotic system, we have developed a random number generator (RNG) for practical image encryption applications. Furthermore, security analyses are carried out with the RNG and image encryption designs.

SUMMARYThe research on the su cient criterion for chaos synchronization of the master-slave Chua's circuits by linear state error feedback control has received much attention and some synchronization criteria for special control matrix were proposed. In this paper, the above synchronization issue is investigated in the situation of general linear state error feedback controller with propagation delay of control signals from the master Chua's circuit. First of all, a master-slave synchronization scheme for Chua's circuits with propagation delay is given and the relevant error system is derived. Using a quadratic Lyapunov function and frequency domain method, three new algebraic synchronization criteria for the synchronization scheme with general control matrix are proven. They are applied to derive the synchronization criteria for simple control matrices. Some examples are given to show the sharpness of these new criteria compared with the known criteria.