Generation of Extremely Multistable Systems Based on Lurie Systems
| Autor: | I. M. Burkin, O. I. Kuznetsova |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematical model
business.industry General Mathematics 010102 general mathematics MathematicsofComputing_NUMERICALANALYSIS Chaotic Lyapunov exponent Topology Encryption Dynamical system 01 natural sciences 010305 fluids & plasmas Image (mathematics) Nonlinear Sciences::Chaotic Dynamics symbols.namesake Development (topology) 0103 physical sciences Attractor symbols 0101 mathematics business Mathematics |
| Zdroj: | Vestnik St. Petersburg University, Mathematics. 52:342-348 |
| ISSN: | 1934-7855 1063-4541 |
| DOI: | 10.1134/s1063454119040034 |
| Popis: | Chaotic signals and systems are widely used in image encryption, secure communications, weak signal detection, and radar systems. Many researchers have focused in recent years on the development of systems with an infinite number of coexisting chaotic attractors. We propose some approaches in this work to the generation of self-reproducing systems with an infinite number of coexisting self-excited or hidden chaotic attractors with the same Lyapunov exponents based on mathematical models of Lurie systems. The proposed approach makes it possible to generate extremely multistable systems using numerous known examples of the existence of chaotic attractors in Lurie systems without resorting to an exhaustive computer search. We illustrate the proposed methods by constructing extremely multistable systems with 1-D and 2-D grids of hidden chaotic attractors using the generalized Chua system, in which hidden attractors were first discovered by G.A. Leonov and N.V. Kuznetsov. |
| Databáze: | OpenAIRE |
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