Denis Butusov
Saint-Petersburg Electrotechnical University “LETI”, Russia.
Abstract: In this talk, recent achievements in controlling the properties of chaotic systems are to be presented. The lecture will guide the auditory from the definition of well-known symmetric integration methods to possible ways to control the stability of digital chaotic maps and discrete models of continuous systems using discrete operators with adaptive symmetry. First, the new technique to control the multistability in the discrete models of chaotic systems will be demonstrated. The controllable multistability in the discrete model of Chua circuit with memristor will be shown through bifurcation, initial conditions, and Lyapunov spectrum analysis. Next, the possibility to artificially induce multistability in the finite-difference models of continuous chaotic systems will be shown. The adaptive models of Lorenz and Chen systems are to be considered as representative examples of this phenomenon.
Finally, some applications of the proposed approach, including chaos-based cryptography, nonlinear control, and simulation of distributed objects by lattices of discrete maps with controllable stability, will be considered. The talk ends with a brief overview of prominent directions for further research.