On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications

Abstract

In this paper we deal with the projective synchronization (PS) of hyperchaotic complex nonlinear systems and its application in secure communications based on passive theory. The unpredictability of the scaling factor in PS can additionally enhance the security of communications. In this paper, a scheme for secure message transmission is proposed, and we try to transmit more than one large or bounded message from the transmitter to the receiver. The new hyperchaotic complex Lorenz system is employed to encrypt these messages. In the transmitter, the original messages are modulated into its parameter. In the receiver, we assume that the parameter of the receiver system is uncertain. The controllers and corresponding parameter update law are constructed to achieve PS between the transmitter and receiver system with an uncertain parameter, and identify the unknown parameter via passive theory. The original messages can be recovered successfully through some simple operations by the estimated parameter. Numerical results have verified the effectiveness and feasibility of the presented method.

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

“…Different synchronization schemes for chaotic systems were studied and investigated [6][7][8][9][10]. Among these schemes, hybrid synchronization [11][12][13][14][15][16][17][18][19] is one in which some of the chaotic systems are synchronized whereas others are antisynchronized.…”

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

“…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.…”

Circuit Simulation of an Analog Secure Communication based on Synchronized Chaotic Chua’s System

“…For the chaotic encryption, which is similar to the principle of symmetric encryption [9], synchronization, commonly known as synchronization of chaos since the work of Pecora and Carroll during the early 90 [10] [11], is ensured by observers [12] [13,14,15,16]. Others approaches have been proposed in the open literature to synchronize two chaotic systems [17,18,19,20,21,22], using passive control [23,24,25], or impulsive control [26].…”