Chaotic Characteristics of Discrete-time Linear Inclusion Dynamical Systems

In this paper, we study the chaotic behavior of a discrete-time linear inclusion.Comment: 7 pages; submitte

Discrete-time synchronization of chaotic systems for secure communication

This paper deals with the problem of designing an exact nonlinear reconstructor for discrete-time chaotic encrypted messages. More precisely, we investigate the problem of designing a discrete-time dead-beat observer for nonlinear systems with unknown inputs. The application of the proposed observer in the context of secure communication and data transmission is also investigated

Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.Comment: submitted to EP