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Abstract Chaotic and hyperchaotic systems with interesting behaviors have been of interest in the recent years. In this paper we introduce a hyperchaotic memristor oscillator which shows both stable and unstable fixed points. Such systems have been less investigated in the literatures. It should also to be noted that the proposed hyperchaotic system has only one nonlinearity which is a flux controlled memristor. Depending on the control parameter, the system displays different behaviors and coexisting attractors. A linear quadratic regulator based synchronization of the proposed hyperchaotic system is designed and numerically analyzed. We also design such a fuzzy based PID controller for chaos control in such a memristor oscillator. [ABSTRACT FROM AUTHOR]

Four-dimensional chaotic systems are a very interesting topic for researchers, given their special features. This paper presents a novel fractional-order four-dimensional chaotic system with self-excited and hidden attractors, which includes only one constant term. The proposed system presents the phenomenon of multi-stability, which means that two or more different dynamics are generated from different initial conditions. It is one of few published works in the last five years belonging to the aforementioned category. Using Lyapunov exponents, the chaotic behavior of the dynamical system is characterized, and the sensitivity of the system to initial conditions is determined. Also, systematic studies of the hidden chaotic behavior in the proposed system are performed using phase portraits and bifurcation transition diagrams. Moreover, a design technique of a new fuzzy adaptive sliding mode control (FASMC) for synchronization of the fractional-order systems has been offered. This control technique combines an adaptive regulation scheme and a fuzzy logic controller with conventional sliding mode control for the synchronization of fractional-order systems. Applying Lyapunov stability theorem, the proposed control technique ensures that the master and slave chaotic systems are synchronized in the presence of dynamic uncertainties and external disturbances. The proposed control technique not only provides high performance in the presence of the dynamic uncertainties and external disturbances, but also avoids the phenomenon of chattering. Simulation results have been presented to illustrate the effectiveness of the presented control scheme. • A novel fractional-order four-dimensional chaotic system with self-excited and hidden attractors is introduced. • We have characterized the chaos of the dynamical system and determined the sensitivity of the system. • Systematic studies of the hidden chaotic behavior in the proposed system are performed. • We have designed a fuzzy adaptive sliding mode control to synchronize the proposed system. [ABSTRACT FROM AUTHOR]

In this paper, a color image encryption algorithm is presented, the new algorithm uses double-layer Joseph's scramble, XOR diffusion, and is built on a laser chaos system. Firstly, a laser chaotic system is chosen in the scheme and it has the advantages of extended bandwidth and rapid propagation speed. Secondly, the structure of the image encryption scheme follows the Fridrich structure. In the scrambling part, a modified Joseph's ring is adapted to process the chaotic sequence and the picture pixel sequence to achieve the scrambling of the plaintext image pixel positions. In the diffusion part, the XOR diffusion technique is employed to reduce the statistical characteristics of the plaintext picture, which can resist external attacks better. Finally, the presented encryption algorithm is demonstrated utilizing simulation results and security analysis. The simulation performance demonstrates that the new proposed method is practical. The security test performance indicates that the algorithm can validly encrypt the image with good security performance. In summary, the new scheme designed in this paper can offer better technical backing for the wide applications of image encryption. [ABSTRACT FROM AUTHOR]