Ikeda map

Abstract: The evolution of wireless and mobile communication from 0G to the upcoming 5G gives rise to data sharing through the Internet. This data transfer via open public networks are susceptible to several types of attacks. Encryption is a method that can protect information from hackers and hence confidential data can be secured through a cryptosystem. Due to the increased number of cyber attacks, encryption has become an important component of modern-day communication. In this article, a new image encryption algorithm is presented using chaos theory and dynamic substitution. The proposed scheme is based on two-dimensional Henon, Ikeda chaotic maps, and substitution box (S-box) transformation. Through Henon, a random S-Box is selected and the image pixel is substituted randomly. To analyze security and robustness of the proposed algorithm, several security tests such as information entropy, histogram investigation, correlation analysis, energy, homogeneity, and mean square error are performed. The entropy values of the test images are greater than 7.99 and the key space of the proposed algorithm is 2 798 . Furthermore, the correlation values of the encrypted images using the proposed scheme are close to zero when compared with other conventional schemes. The number of pixel change rate (NPCR) and unified average change intensity (UACI) for the proposed scheme are higher than 99.50% and 33, respectively. The simulation results and comparison with the state-of-the-art algorithms prove the efficiency and security of the proposed scheme.

Abstract: This paper is concerned with a fractional Caputo-difference form of Ikeda map. The dynamics of the proposed map is investigated numerically through phase plots and bifurcation diagrams considered from different perspectives. In addition, a stabilization controller is proposed and the asymptotic convergence of the states is established using the stability theory of linear fractional-order discrete systems. Furthermore, a new synchronization scheme is introduced whereby a new 2D fractional-order chaotic map is considered as the master system and the fractional-order Ikeda map is considered as the response system. Experimental investigations and numerical simulations are also provided to confirm the main findings of the study.

Abstract: Using time delay coordinates and assuming no a priori knowledge of the dynamical system, we propose a method that stabilizes a desired periodic orbit embedded in a chaotic attractor. Similar to the original control algorithm introduced by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)], the stabilization is done via small time dependent perturbations of an accessible control parameter. The control method is numerically illustrated using both the Ikeda map, which describes the dynamics of a nonlinear laser cavity and the double rotor map which describes a periodically kicked dissipative mechanical system.