This work investigates chaos synchronization between two different fractional order chaotic systems of Lorenz family. The fractional order Lü system is controlled to be the fractional order Chen system, and the fractional order Chen system is controlled to be the fractional order Lorenzlike system. The analytical conditions for the synchronization of these pairs of different fractional order ch...

Abstract. The paper firstly analyzes the fractional-order Chen system by using function approximation in frequency domain and time domain respectively, gives its Lyapunov exponents and bifurcation diagrams, and shows its chaotic characteristics from numerical analysis point of view. Then, based on fractional-order frequency domain approximation, two different analog circuits are designed to imp...

We investigate a discrete-time Chen system. First, we give the topological classifications of fixed points this Then, analytically show that discrete system underlies Neimark–Sacker (NS) bifurcation and period doubling (PD) under specific parametric circumstances. confirm existence PD NS via explicit PD-NS criterion determine direction both bifurcations with help center manifold theory. perform...

where a, b, c ∈ R are parameters is known as the Chen system [Chen & Ueta, 1999]. It exhibits chaotic phenomena which resembles some familiar features from both the Lorenz and the Rössler attractors, for suitable choices of the parameters. Despite of its similar structure to the Lorenz system, it is not topologically equivalent. This is why Lü and Chen investigated the real differential system

In many situations, the existence of several equilibrium points in a dynamical system makes its dynamics more complex and allows some special structures. Examples include the well-known multiscroll attractors ([Wang, 2009; Qi et al., 2008; Liu & Chen, 2004; Li, 2008; Wang et al., 2009; Lü et al., 2008; Yu et al., 2006; Yu et al., 2008, 2010a; Wang & Chen, 2012] and references therein) such as c...

In this paper, a new method is presented for encryption of colored images. This method is based on using stack data structure and chaos which make the image encryption algorithm more efficient and robust. In the proposed algorithm, a series of data whose range is between 0 and 3 is generated using chaotic logistic system. Then, the original image is divided into four subimages, and these four i...

The chaotic behavior of the Rabinovich–Fabrikant system, a model with multiple topologically different chaotic attractors, is analyzed. Because of the complexity of this system, analytical and numerical studies of the system are very difficult tasks. Following the investigation of this system carried out in [Danca & Chen, 2004], this paper verifies the presence of multiple chaotic attractors in...

This paper reports the finding of a simple one-parameter family of three-dimensional quadratic autonomous chaotic systems. By tuning the only parameter, this system can continuously generate a variety of cascading Lorenz-like attractors, which appears to be richer than the unified chaotic system that contains the Lorenz and the Chen systems as its two extremes. Although this new family of chaot...