Chaos Generated From the Fractional-Order Complex Chen System and Its Application to Digital Secure Communication

Abstract

In this paper, a novel dynamic system, the fractional-order complex Chen system, is presented for the first time. Dynamic behaviors of system are studied analytically and numerically. Different routes to chaos are shown, and diverse kinds of motions are identified and exhibited by means of bifurcation diagram, portrait phase and the largest Lyapunov exponent. Secondly, an application to digital secure communication based on the novel system is proposed, in which security is enhanced by continually switching different orders of derivative in an irregular pattern. Furthermore, making full use of the advantage of high-capacity transmission of complex system, the improved digital secure communication scheme is achieved based on hybrid synchronization in coupled fractional-order complex Chen system, that means anti-synchronization in real part of state variables and projective synchronization in imaginary part, respectively. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the proposed schemes.

Adaptive generalized combination complex synchronization of uncertain real and complex nonlinear systems

“…where x = (x 1 , x 2 , · · · x m 1 ) T ∈ R m 1 and y = ( y 1 , y 2 , · · · y m 2 ) T ∈ R m 2 are real state vectors of the drive systems (1) and (2). A = (a 1 , a 2 , · · · a n 1 ) T ∈ R n 1 and B = (b 1 , b 2 , · · · b n 2 ) T ∈ R n 2 are vectors of unknown parameters.…”

“…Hence, the zero solution of the error dynamical system (7) is asymptotically stable, that is to say, AGCCS of the systems (1), (2) and (3) is accomplished. Meanwhile, the estimated values of unknown parameters converge to their true values.…”

“…Compared to chaotic real systems, chaotic complex systems exhibit more abundant and complicated dynamical behaviors with strong unpredictability, which can be applied to chaos secure communication for the sake of higher signal transmission efficiency and secure performance. [2][3][4] Therefore, much attention and many efforts are devoted to investigate synchronization of chaotic complex systems in recent years, and various synchronization schemes have been proposed and realized successfully, such as complete synchronization, 5,6 antisynchronization, 7,8 lag synchronization, 9,10 phase synchronization, 11 projective synchronization, 12,13 and their extended synchronization schemes. [14][15][16][17][18][19] All of the above-mentioned synchronization methods are designed for one drive system and one response system.…”

Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos

“…Lots of classical fractional-order real hyper-chaotic (chaotic) systems can be formed as system (7), such as the fractional-order real Chua system [7], the fractional-order real hyper-chaotic Rössler system [8], the fractional-order real Liu system [9] and other fractional-order real Lorenz-like systems [10]. Lots of classical fractional-order complex chaotic systems can be formed as system (8), such as fractional-order complex Lorenz system [15] and fractional-order complex Chen system [16].…”

“…In 2013, Luo and Wang introduced a fractional-order Lorenz system [15] and Chen system [16] in complex space and investigated their application to digital secure communication, where the complex variables increase the content of transmitting information signals and enhance their security further.…”