Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer
Lazaros Moysis,
Christos Volos,
Viet-Thanh Pham,
Sotirios Goudos,
Ioannis Stouboulos,
Mahendra Kumar Gupta,
Vikas Kumar Mishra
Affiliations
Lazaros Moysis
Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Christos Volos
Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Viet-Thanh Pham
Faculty of Electrical and Electronic Engineering, Phenikaa Institute for Advanced Study (PIAS), Phenikaa University, Yen Nghia, Ha Dong district, Hanoi 100000, Vietnam
Sotirios Goudos
Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Ioannis Stouboulos
Laboratory of Nonlinear Systems, Circuits & Complexity (LaNSCom), Physics Department, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Mahendra Kumar Gupta
Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, India
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.
