This article proposes a fast reaching finite time synchronization approach for chaotic systems along with its application to medical image encryption. First, an adaptive terminal sliding mode tracking approach with fast reaching condition is designed to synchronize the chaotic systems at the transmitter and receiver ends in finite time. Then, a chaotic cryptosystem, using synchronized chaotic systems as secret keys generator, is proposed to enhance the security of medical image transmission and/or storage. The applicability and efficiency of the proposed synchronization approach is assessed using a simulation as well as an analytical study. The analysis encompassed security tools such as histogram analysis, correlation test, and information entropy change the rate of the number of pixels and unified average changing intensity. The obtained results confirmed the robustness and fast convergence rate of the proposed synchronization approach. The security analysis also shows that the proposed cryptosystem displays acceptable levels of resistance to various attacks.

This paper proposes a finite time chaos synchronization approach for the secure communication of satellite imaging. To this end, chaotic oscillators are considered in both the transmitter and receiver ends to generate the chaotic encryption/decryption keys. To mitigate the non-negligible channel time-delay between the receiver and transmitter, we propose a robust controller design. The proposed approach is designed based on the Lyapunov stability theory and the finite-time synchronization concept to attain finite time synchronization in a time-delayed channel. By using synchronized chaotic keys, a physical-layer chaotic encryption scheme for transmitting the satellite images is designed in orthogonal frequency-division multiplexing wireless network. The proposed chaotic-based satellite image encryption/decryption system is validated using a numerical simulation study. Additionally, to analyse the robustness and demonstrate the efficiency of the proposed chaotic encryption structure, a set of security analysis tools such as histogram analysis, key space analysis, correlation test, information entropy and other statistical analysis were performed.

In this work, we studied the complex behaviors of the fractional-order financial chaotic system, consisting of a simple, relatively chaotic system with two quadratic nonlinearities (QN) and a sextic nonlinearity (SN). We completed and enriched the results presented in the study of Subartini et al. (2021). As a result of this, our study focused more on the fractional order and adaptive finite-time sliding mode control in the financial risk chaotic system. The dynamical behaviors of the financial chaotic system (FCS) with two QN and an SN were analyzed, and the stability was investigated via the Cardano method. The stability analysis showed that the real part of all the roots was negative, which confirmed the stability of the new system under the typical parameters. By using the MATLAB simulation, these properties were characterized, including the phase portraits, 0-1 test, Poincaré map, bifurcation diagram, and Lyapunov exponent. The analysis showed that the financial risk chaotic system of fractional order was able to exhibit chaotic behavior and periodical behavior. In spite of external perturbations and uncertainty, an adaptive finite-time sliding mode control strategy was devised to guide the states of the financial chaotic system to the origin in a finite amount of time. MATLAB phase plots were employed in this study to illustrate all the main results.

This study proposes a nonsingular barrier-function-based terminal sliding mode control technique for nth-order nonlinear dynamic systems. Its main objective is to guarantee the finite-time tracking performance in the presence of unmodeled dynamics, external disturbances and parameter variations. The proposed approach is synthesized using a novel barrier function-based terminal sliding surface to ensure the effective estimation of the system perturbations using the barrier adaptation laws, and thereby achieve the desired tracking performance. The dynamics of chaotic models are strongly dependent upon the initial conditions, parameters of the system, parametric uncertainty and external disturbances which are required to be controlled/synchronized by a robust nonlinear control technique. By designing the terminal sliding mode control approach combined with the adaptive control law, the tracking problem of the nth-order nonlinear dynamical system with unmodeled dynamics, parametric variations and external disturbances is investigated. Moreover, the application of the proposed method is studied using the color-image scrambling system. The scrambling keys are created by transmitter chaotic systems, where using the chaotic keys and scrambling techniques, the original color image is encrypted. The performance and applicability of the proposed design is assessed using two practical applications: a chaotic hyper-jerk system and a color image encryption system. The simulation and analytical results obtained with both systems confirmed the ability of the proposed control method to guarantee the finite time convergence of sliding surface, ensure chattering-free dynamics and avoid the singularity problems.