Symmetry in Chaotic Systems and Circuits

Symmetry can play an important role in the field of nonlinear systems and especially in the design of nonlinear circuits that produce chaos. Therefore, this Special Issue, titled “Symmetry in Chaotic Systems and Circuits”, presents the latest scientific advances in nonlinear chaotic systems and circuits that introduce various kinds of symmetries. Applications of chaotic systems and circuits with symmetries, or with a deliberate lack of symmetry, are also presented in this Special Issue. The volume contains 14 published papers from authors around the world. This reflects the high impact of this Special Issue

A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility

Probing 3D chaotic Thomas’ cyclically attractor with multimedia encryption and electronic circuitry

This study investigates Thomas’ cyclically symmetric attractor dynamics with mathematical and electronic simulations using a proportional fractional derivative to comprehend the dynamics of a given chaotic system. The three-dimensional chaotic flow was examined in detail with Riemann-Liouville derivative for different values of the fractional index to highlight the sensitivity of chaotic systems with initial conditions. Thus, the dynamics of the fractional index system were investigated with Eigenvalues, Kaplan–Yorke dimension, Lyapunov exponent, and NIST testing, and their corresponding trajectories were visualized with phase portraits, 2D density plot, and Poincaré maps. After obtaining the results, we found that the integer index dynamics are more complex than the fractional index dynamics. Furthermore, the chaotic system circuit is simulated with operational amplifiers for different fractional indices to generate analog signals of the symmetric attractor, making it an important aspect of engineering. The qualitative application of our nonlinear chaotic system is then applied to encrypt different data types such as voice, image, and video, to ensure that the developed nonlinear chaotic system can widely applied in the field of cyber security

Fractional-Order Analysis of Modified Chua’s Circuit System with the Smooth Degree of 3 and Its Microcontroller-Based Implementation with Analog Circuit Design

In the paper, we futher consider a fractional-order system from a modified Chua’s circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua’s circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua’s circuit with the piecewise-smooth continuous system

Speech signal compression and encryption based on sudoku, fuzzy C-means and threefish cipher

Compression and encryption of speech signals are essential multimedia technologies. In the field of speech, these technologies are needed to meet the security and confidentiality of information requirements for transferring huge speech signals via a network, and for decreasing storage space for rapid retrieval. In this paper, we propose an algorithm that includes hybrid transformation in order to analyses the speech signal frequencies. The speech signal is then compressed, after removing low and less intense frequencies, to produce a well compressed speech signal and ensure the quality of the speech. The resulting compressed speech is then used as an input in a scrambling algorithm that was proposed on two levels. One of these is an external scramble that works on mixing up the segments of speech that were divided using Fuzzy C-Means and changing their locations. The internal scramble scatters the values of each block internally based on the pattern of a Sudoku puzzle and quadratic map so that the resulting speech is an input to a proposed encryption algorithm using the threefish algorithm. The proposed algorithm proved to be highly efficient in the compression and encryption of the speech signal based on approved statistical measures

A novel four-wing chaotic system with multiple equilibriums: Dynamical analysis, multistability, circuit simulation and pseudo random number generator (PRNG) based on the voice encryption

Recently, there has been tremendous interest worldwide in the possibility of using chaos in communication systems. Many different chaos-based secure communication schemes have been proposed up until now. However, systems with strong chaoticity are more suitable for chaos-based secure communication. From the viewpoint of Lyapunov exponents, a chaotic system with a larger positive Lyapunov exponent is said to be more complex. This paper constructing a multistable chaotic system that can produce coexisting attractors is an attractive field of research due to its theoretical and practical usefulness. An innovative 3D dynamical system is presented in this research. It can display various coexisting attractors for the same values of parameters. The new system is more suitable for chaos-based applications than recently reported systems since it exhibits strong multistable chaotic behavior, as proved by its large positive Lyapunov exponent. Furthermore, the accuracy of the numerical calculation and the system's physical implementations are confirmed by analog circuit simulation. Finally, implementing the proposed voice encryption is done using a four-wing chaotic system based on the PRNG