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Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

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  • Ruofeng Rao

    (Department of Mathematics, Chengdu Normal University, Chengdu 61130, China
    Institute of Financial Mathematics, Chengdu Normal University, Chengdu 61130, China)

Abstract

The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

Suggested Citation

  • Ruofeng Rao, 2019. "Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate," Mathematics, MDPI, vol. 7(7), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:579-:d:244091
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    References listed on IDEAS

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    1. Luo, Mengzhuo & Liu, Xinzhi & Zhong, Shouming & Cheng, Jun, 2018. "Synchronization of stochastic complex networks with discrete-time and distributed coupling delayed via hybrid nonlinear and impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 381-393.
    2. Zeng, Deqiang & Pu, Zhilin & Zhang, Ruimei & Zhong, Shouming & Liu, Yajuan & Wu, Guo-Cheng, 2019. "Stochastic reliable synchronization for coupled Markovian reaction–diffusion neural networks with actuator failures and generalized switching policies," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 88-106.
    3. Rongyan Zhang, 2012. "Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, April.
    4. Yang, Huilan & Wang, Xin & Zhong, Shouming & Shu, Lan, 2018. "Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 75-85.
    5. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
    6. Li, Xiaodi & Shen, Jianhua & Rakkiyappan, R., 2018. "Persistent impulsive effects on stability of functional differential equations with finite or infinite delay," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 14-22.
    7. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
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