A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter. (February 2022)

• Record Type: Journal Article
• Authors: Yang, Jing; Hou, Xiaorong; Li, Xiaoxue; Luo, Min
• Is Part Of: Chaos, solitons and fractals. Volume 155(2022)
• Publication Date: 2022-02
• Subjects: Hopf bifurcation -- Multiple-parameter -- Fractional-order systems -- Nonlinear system -- Parameter space method; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111714
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Hopf bifurcation conditions of system with multiple-parameter are given. A parameter space method for analyzing Hopf bifurcation is proposed. A parameter space method for analyzing stability is proposed. Abstract: Hopf bifurcation analysis of fractional-order nonlinear systems with multiple-parameter is discussed in this paper. The regions and boundaries corresponding to Hopf bifurcation conditions are described in parameter space. Based on cylindrical algebraic decomposition, the parameter space is decomposed into finite number of connected regions by some boundaries. Then parameter space method is proposed to determine stable parameter region and Hopf bifurcation parameter hypersurface. One example illustrates the effectiveness of the method.