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Hopf Bifurcation and Chaos of a Delayed Finance System

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  • Xuebing Zhang
  • Honglan Zhu

Abstract

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

Suggested Citation

  • Xuebing Zhang & Honglan Zhu, 2019. "Hopf Bifurcation and Chaos of a Delayed Finance System," Complexity, Hindawi, vol. 2019, pages 1-18, January.
    • Handle: RePEc:hin:complx:6715036
    DOI: 10.1155/2019/6715036
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    Cited by:

    1. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    2. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.
    3. Vsevolod G. Sorokin & Andrei V. Vyazmin, 2022. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration," Mathematics, MDPI, vol. 10(11), pages 1-39, May.
    4. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Zizhen Zhang & Fangfang Yang & Wanjun Xia, 2019. "Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    6. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    7. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
    8. Dai, Qinrui & Rong, Mengjie & Zhang, Ren, 2022. "Bifurcations and multistability in a virotherapy model with two time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 289-311.
    9. He, Ke & Shi, Jianping & Fang, Hui, 2024. "Bifurcation and chaos analysis of a fractional-order delay financial risk system using dynamic system approach and persistent homology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 253-274.
    10. Changjin Xu & Maoxin Liao & Peiluan Li & Qimei Xiao & Shuai Yuan, 2019. "Control Strategy for a Fractional-Order Chaotic Financial Model," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    11. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.

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