Designing an M-dimensional nonlinear model for producing hyperchaos. (September 2018)

• Record Type: Journal Article
• Authors: Natiq, Hayder; Banerjee, Santo; He, Shaobo; Said, M.R.M.; Kilicman, Adem
• Is Part Of: Chaos, solitons and fractals. Volume 114(2018)
• Page Start: 506
• Page End: 515
• Publication Date: 2018-09
• Subjects: High-dimensional systems -- Hyperchaotic behavior -- No equilibria -- Stability -- Complexity; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2018.08.005
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: This paper proposes an M-dimensional nonlinear hyperchaotic model (M-NHM) for producing new discrete-time systems with complex hyperchaotic behaviors. The M-NHM is constructed by designing an M-dimensional nonlinear system ( M ≥ 2) to generate a chaotic behavior. To enhance the nonlinearity of M-NHM, hence changing its behavior to hyperchaotic, an iterative chaotic map with infinite collapse (ICMIC) is composed. Mathematical analysis shows that the M-NHM has either no equilibria, or an arbitrarily large number of equilibria. Moreover, Routh−Hurwitz criterion reveals that all these equilibria are unstable when M ≥ 3. To investigate the dynamical properties and complexity of the M-NHM, we provide 2-NHM and 3-NHM as typical examples. Simulation results show that the 2-NHM and 3-NHM have good ergodicity, wide hyperchaotic behavior, highly sensitivity dependence, and high complexity. With all these features, the M-NHM would be an ideal model for secure communications and other engineering applications.