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

A New Class of Two-dimensional Chaotic Maps with Closed Curve Fixed Points

This is the author accepted manuscript. The final version is available from World Scientific Publishing via the DOI in this recordThis paper constructs a new class of two-dimensional maps with closed curve fixed points. Firstly, the mathematical model of these maps is formulated by introducing a nonlinear function. Different types of fixed points which form a closed curve are shown by choosing proper parameters of the nonlinear function. The stabilities of these fixed points are studied to show that these fixed points are all non-hyperbolic. Then a computer search program is employed to explore the chaotic attractors in these maps, and several simple maps whose fixed points form different shapes of closed curves are presented. Complex dynamical behaviours of these maps are investigated by using the phase-basin portrait, Lyapunov exponents, and bifurcation diagrams.National Natural Science Foundation of ChinaNatural Science Foundation of Jiangsu Province of China5th 333 High-level Personnel Training Project of Jiangsu Province of ChinaExcellent Scientific and Technological Innovation Team of Jiangsu UniversityJiangsu Key Laboratory for Big Data of Psychology and Cognitive Scienc

A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control

Entropy analysis and image encryption application based on a new chaotic system crossing a cylinder

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents' spectrum, and entropy measurement. Bifurcation analysis of the proposed system with two initiation methods reveals its multistability. As an engineering application, the system's efficiency is tested in image encryption. The complexity of the chaotic attractor of the proposed system makes it a proper choice for encryption. States of the chaotic attractor are used to shue the rows and columns of the image, and then the shued image is XORed with the states of chaotic attractor. The unpredictability of the chaotic attractor makes the encryption method very safe. The performance of the encryption method is analyzed using the histogram, correlation coefficient, Shannon entropy, and encryption quality. The results show that the encryption method using the proposed chaotic system has reliable performance. - 2019 by the authors.Scopu

S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium

Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented