Accurate Synchronization of Digital and Analog Chaotic Systems by Parameters Re-Identification

Abstract

The verification of the digital models of chaotic systems and processes is a valuable problem in many practical applications, such as nonlinear control and communications. In our study, we propose a hybrid technique for chaotic systems' identification, based on the chaotic synchronization of digital and analog counterparts and a numerical optimization method used for the fine tuning of parameters. An analog circuit implementing the Rössler oscillator with digitally controlled parameters was chosen as an identification object, and the FPGA model was used as a digital counterpart for coupling and parameter retrieval. The synchronization between analog and digital chaotic models can be used to estimate the quality of an identification procedure. The results of this study clarify the practical bounds of digital and analog systems' equivalence. They also contribute to the problem of designing technical systems possessing advantages of both analog and digital chaotic generators (e.g., a high accuracy and protection from quasi-chaotic oscillation modes).

Synthetic Adaptive Fuzzy Disturbance Observer and Sliding-Mode Control for Chaos-Based Secure Communication Systems

“…The synchronization of electronic circuits is found in [17][18][19][20]. The synchronization of digital and analog chaotic systems was discussed in [21][22]. We recently proposed a new disturbance observer based on D-stability for synchronizing two nonidentical T-S fuzzy chaotic systems.…”

FPGA-based Chaotic Cryptosystem by Using Voice Recognition as Access Key

“…and it is implemented in FPGA by using the SysGen ToolBox in Matlab's Simulink. Figure 4 depicts the block diagram of the mod(255) operation implemented in the FPGA, based on Equations (1) and (2). Equation (1) contemplates the x n variable that corresponds to one of the states of the equations on differences that describe the respective chaotic map, which are represented by real numbers of a fixed point in the FPGA.…”

“…Chaotic systems have shown their usefulness in practical applications focused on security, and they have been implemented with different kinds of electronic devices [1][2][3][4]. In the case of designing cryptosystems, currently one can found different encryption standards, such as: TDES (Triple Data Encryption Standard), ASD (Advanced Encryption Standard), Blowfish and IDEA (International Data Encryption Standard), from which one must be aware that when attacked with dedicated software, they show weaknesses under certain conditions.…”

A Novel Image Encryption Scheme Based on 2D Fractional Chaotic Map, DWT and 4D Hyper-chaos

“…So far, based on the above 1D chaotic maps, such as the Logistic map and the Tent map [22][23][24], and 2D chaotic systems, such as the Henon map [25][26][27][28], and 3D chaotic systems such as the Rossler chaotic attractor [29,30], the Chua chaotic system [31,32] and the Chen chaotic system [33][34][35], the applications of chaotic systems in image encryption schemes have been relatively mature in chaos researches and developments. However, the fractional-order chaotic systems have more complex dynamic behaviors and mathematical explanations than the above integer order chaotic systems, so they have higher degrees of non-linearity [36].…”