Search Results (5)

The Shimizu–Morioka dynamical system is analytically investigated in this paper by means of the Optimal Auxiliary Functions Method (OAFM). This system has a chaotic dynamical behavior, specified for more physical applications as chaos synchronization, an attractive phenomenon involving various real-life processes. Semi-analytical solutions for the Shimizu–Morioka system are provided. A comparative analysis between the obtained results via the OAFM method and the corresponding numerical solution highlights the accuracy and efficiency of the involved method. The choice of the OAFM method is justified by the performance in comparison with the iterative method with 7–10 iterations. The physical parameters’ influence is investigated on damped oscillations and periodical behaviors of the obtained solutions. Full article

This study presents an innovative approach utilizing the new Shimizu–Morioka chaotic system. By integrating adaptive backstepping control with GYC partial region stability theory, we successfully achieve synchronization of a slave system with the proposed Shimizu–Morioka chaotic system. The architecture, encompassing the chaotic master system, synchronized slave system, adaptive backstepping controllers, and parameter update laws, has been implemented on an FPGA platform. Comparative analysis demonstrates that the synchronization convergence times (e1, e2, e3, and e4) are significantly reduced compared to conventional adaptive backstepping control methods, exhibiting speed enhancements of approximately 3.42, 3.55, 5.89, and 9.23 times for e1, e2, e3, and e4, respectively. Furthermore, the synchronization results obtained from continuous-time, discrete-time systems, and FPGA implementations exhibit consistent outcomes, validating the effectiveness of the proposed model and controller. Leveraging this validated synchronization framework, chaotic synchronization and secure image encryption are successfully implemented on the FPGA platform. The chaotic signal circuits are meticulously designed and integrated into the FPGA to facilitate a robust image encryption algorithm. In this system, digital signals generated by the synchronized slave chaotic system are utilized for image decryption, while the master chaotic system’s digital signals are employed for encryption. This dual-system architecture highlights the efficacy of the chaotic synchronization method based on the novel Shimizu–Morioka system for practical applications in secure communication. Full article

An exploding demand for processing capabilities related to the emergence of the Internet of Things (IoT), Artificial Intelligence (AI), and big data, has led to the quest for increasingly efficient ways to expeditiously process the rapidly increasing amount of data. These ways include different approaches like improved devices capable of going further in the more Moore path but also new devices and architectures capable of going beyond Moore and getting more than Moore. Among the solutions being proposed, Stochastic Computing has positioned itself as a very reasonable alternative for low-power, low-area, low-speed, and adjustable precision calculations—four key-points beneficial to edge computing. On the other hand, chaotic circuits and systems appear to be an attractive solution for (low-power, green) secure data transmission in the frame of edge computing and IoT in general. Classical implementations of this class of circuits require intensive and precise calculations. This paper discusses the use of the Stochastic Computing (SC) framework for the implementation of nonlinear systems, showing that it can provide results comparable to those of classical integration, with much simpler hardware, paving the way for relevant applications. Full article

Nowadays, the dynamics of non-integer order system or fractional modelling has become a widely studied topic due to the belief that the fractional system has hereditary properties. Hence, as part of understanding the dynamic behaviour, in this paper, we will perform the computation of stability criterion for a fractional Shimizu–Morioka system. Different from the existing stability analysis for a fractional dynamical system in literature, we apply the optimal Routh–Hurwitz conditions for this fractional Shimizu–Morioka system. Furthermore, we introduce the way to calculate the range of adjustable control parameter $\beta$ to obtain the stability criterion for fractional Shimizu–Morioka system. The result will be verified by using the predictor-corrector scheme to obtain the time series solution for the fractional Shimizu–Morioka system. The findings of this study can provide a better understanding of how adjustable control parameter $\beta$ influences the stability criterion for fractional Shimizu–Morioka system. Full article

In applied investigations, the invariance of the Lyapunov dimension under a diffeomorphism is often used. However, in the case of irregular linearization, this fact was not strictly considered in the classical works. In the present work, the invariance of the Lyapunov dimension under diffeomorphism is demonstrated in the general case. This fact is used to obtain the analytic exact upper bound of the Lyapunov dimension of an attractor of the Shimizu–Morioka system. Full article