In this letter, a new four-dimensional continuous autonomous hyperchaotic system, which is constructed based on a modified finance system by introducing a nonlinear state feedback controller. The detailed dynamical behaviors of this hyperchaotic system are further investigated, including equlibria and stability, various attractors, bifurcation analysis, and Lyapunov exponents spectrum. Furtherm...

A systematic circuit design approach is proposed for experimental verification of hyperchaotic 2-, 3-, 4-scroll attractors from a generalized Matsumoto–Chua–Kobayashi (MCK) circuit. Moreover, using appropriate discrete and extended transformations, a novel digital signal processor (DSP) method is also presented for physically realizing the above hyperchaotic 2-, 3-, 4-scroll attractors. This is...

This paper proposes a new four-dimensional continuous autonomous hyperchaotic system, which is constructed based on the Lü system by introducing a nonlinear state feedback controller. Some dynamical properties, including equlibria, stability, Lyapunov exponents spectrum and bifurcation, of this hyperchaotic system are investigated in detail. Moreover, a novel analog circuit is also designed for...

We have applied a famous engineering method, called model reference control, to control hyperchaos. We have proposed a general description of the hyperchaotic system and its reference system. By using the Lyapunov stability theorem, we have obtained the expression of the controller. Four examples for the both certain case and the uncertain case show that our method is very effective for control...

A new memristive system is presented in this paper. The peculiarity of the model is that it does not display any equilibria and exhibits periodic, chaotic, and also hyperchaotic dynamics in a particular range of the parameters space. The behavior of the proposed system is investigated through numerical simulations, such as phase portraits, Lyapunov exponents, and Poincaré sections, and circuita...

The substitution box (S-box) is found in many block cipher, and it is a very important component. Since the chaotic system has several significant advantageous properties desirable for cryptosystem, the design of S-box using chaos has attracted a great deal of attention in recent years. In this paper, a novel method for designing key-dependent S-boxes based on a four-dimensional hyperchaotic Ch...

A simple electronic system exhibiting hyperchaotic behaviour is described. The system includes two nonlinearly coupled 2nd order unstable oscillators, each composed of an LC resonance loop and an amplifier. The system is investigated by means of numerical integration of appropriate differential equations, PSPICE simulations and hardware experiments. The Lyapunov exponents are presented to confi...

In this paper, a new hyperchaotic system is constructed via state feedback control. Some basic dynamical properties are studied, such as continuous spectrum, Lyapunov exponents, fractal dimensions, strange attractor and bifurcation diagram of the new hyperchaotic system. In addition, adaptive controllers are designed for stabilizing hyperchaos to unstable equilibrium with the unknown parameters...

This paper studies stability and hybrid synchronization of a time-delay financial hyperchaotic system. Based on Lyapunov stability theorem and differential inequalities, stability is obtained by intermittent linear state feedback control. Furthermore, hybrid synchronization method is firstly proposed to synchronize a financial hyperchaotic system and globally synchronization is obtained by prop...

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple inter...