Neimark–Sacker Bifurcation of Discrete Fractional Chaotic Systems
Fractional chaotic maps have been recently proposed to describe long-memory effects. However, their bifurcation analysis is complicated. This paper considers a linearized system and introduces necessary and sufficient conditions of Neimark–Sacker (N–S) bifurcation by complex analysis method. Both critical values of fractional order and the system’s parameters are determined when the fractional order maps undergo sudden changes. This paper provides an efficient method for the N–S bifurcation analysis of fractional discrete-time systems with time delays.
Authors
- Hu–Shuang Hou (ORCID: https://orcid.org/0000-0003-2681-1082)
- René Lozi (ORCID: https://orcid.org/0000-0003-0451-4255)
- Guo–Cheng Wu (ORCID: https://orcid.org/0000-0002-1946-6770)
Institutions
- Chongqing University of Posts and Telecommunications (CN)
- Université Côte d'Azur (FR)
- Laboratoire de Mathématiques Blaise Pascal (FR)
- Sichuan Normal University (CN)
Publication Details
- Journal
- International Journal of Bifurcation and Chaos
- Published
- 2025-02-28
- DOI
- https://doi.org/10.1142/s021812742550049x
- Citations
- 6
- Primary Topic
- Chaos control and synchronization
- Type
- article
- Field-Weighted Citation Impact
- 7.94
Funders
- Sichuan Youth Science and Technology Foundation
- National Natural Science Foundation of China