This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems...

Recently the engineering community began to seek the possibly application of chaos. The fact that the cryptographic community had used discrete pseudo-chaotic systems for a long time to generate cipher keys that leads to the initiation of applying chaos to secure communications. This paper presents a schematic design methodology for a fuzzy observer based secure communication of hyper chaotic s...

Nowadays a progress in investigation of chaotic dynamics in various branches of science like mechanics, physics, biology, chemistry, medicine, economy, etc. is achieved. In the field of mechanical continuous systems like beams/plates/shells there exists already a vast number of paper devoted to investigation of their bifurcational and chaotic behaviour. For instance, axially accelerating beams ...

This paper presents a new hyper chaos system based on Hénon and Logistic maps which provides characteristics of high capacity, security and efficiency. The Proposed hyper chaos system is employed to generate the key for diffusion in an image encryption algorithm. The simulation experiments to the image encryption algorithm which based on the proposed hyper chaos system show that the algorithm s...

Hyper chaos is the non-periodic behaviour of deterministic nonlinear dynamical system that is highly sensitive to initial conditions with more than one positive Lypunov Exponents, i.e., its dynamics expand not only small line segments, but also small area elements, these giving rise to a ‘thick’ chaotic attractor. Bifurcation effects include the period doubling route to chaos, the intermittency...

We propose a method for controlling chaos and hyper-chaos by applying continuous proportional feedback to the system variables and their derivatives. The method has been applied successfully in six-order coupled Chua’s hyper-chaotic circuit system. The theoretical analysis and numerical simulation results show that unstable fixed points embedded in hyper-chaotic attractors can be stabilized and...

Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization, and quantum dynamics instability. Previous research findings have shown that the OTOCs' exponential growth (EG) marks limit for systems. However, we report this paper a periodically-modulated nonlinear Schr\"odinger system, which interestingly find way of growth: super-EG....

Chaos is a nonlinear behavior that shows chaotic and irregular responses to internal and external stimuli in dynamic systems. This behavior usually appears in systems that are highly sensitive to initial condition. In these systems, stabilization is a highly considerable tool for eliminating aberrant behaviors. In this paper, the problem of stabilization and tracking the chaos are investigated....