Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer

Abstract

In this work a novel chaotic system with a line equilibrium is presented. First, a dynamical analysis on the system is performed, by computing its bifurcation diagram, continuation diagram, phase portraits and Lyapunov exponents. Then, the system is applied to the problem of secure communication. We assume that the transmitted signal is an additional state. For this reason, the nonlinear system is rewritten in a rectangular descriptor form and then an observer is constructed for achieving synchronization and input reconstruction. If we assume some rank conditions (on the nonlinearities and the solvability of a linear matrix inequality (LMI)) on the system matrices then the observer synchronization can be feasible. We evaluate and demonstrate our approach with specific numerical results.

Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs—Application to secure communications

“…Yang et al 38 attractors. 19 This problem refers to the masking of an information signal through a chaotic transmitter system, its secure transmission to a receiver system and its accurate reconstruction, through appropriate signal processing. This problem can be addressed by considering the information signal as an additional system state, which leads to a formulation of the system to rectangular descriptor form.…”

“…[24][25][26][27] A remarkable work has been done by Chakrabarty et al 21 where these nonlinearities have been studied on descriptor systems. Other types of nonlinearities usually being considered in observer design for descriptor systems are Lipschitz, 12,13,19,[28][29][30][31][32] which is the most common, one-sided Lipschitz, 33,34 monotone, [35][36][37] and quadratic inequality. 38 In the following section, Table 1 is given to establish the fact that these nonlinearities fall under the general case considered here.…”

“…Moreover, the case of observer design for rectangular descriptor systems has been considered in several works for the simulation of a secure communications design, utilizing chaotic systems, 14‐17 hyperchaotic, 18 or systems with hidden attractors 19 . This problem refers to the masking of an information signal through a chaotic transmitter system, its secure transmission to a receiver system and its accurate reconstruction, through appropriate signal processing.…”

Darboux Integrability of a Generalized 3D Chaotic Sprott ET9 System

“…Selfexcited attractor are examples such as van der Pol, Belousov-Zhabotinskii, Lorenz, Rössler, Chen, Chua, Lu, Jerk or Sprott's system (case B-S). Various studies of systems with self-excited attractors have been conducted in different science areas especially in engineering applications, like in the design electronic circuits, communications, control systems, and artificial intelligence [16][17][18][19] , Nevertheless, in these systems with the self-excited attractors, there are still various issues that invite further research.…”

A Luenberger-Like Observer for Multistable Kapitaniak Chaotic System

“…Based on the off-line solution of an algebraic Riccati equation, Raghavan and Hedrick proposed an iterative procedure of observer design for a class of Lipschitz nonlinear systems [5]. In [6][7][8][9][10][11], different kinds of observers were studied for chaotic systems. e main use of an observer in chaotic systems is for synchronization [12][13][14][15][16][17][18][19].…”