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Impulsive Stabilization on Hyper-Chaotic Financial System under Neumann Boundary

Author

Listed:
  • Xinggui Li

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Ruofeng Rao

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Xinsong Yang

    (College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China)

Abstract

This paper proposes a novel technique to obtain sufficient conditions for the existence and stabilization of positive solutions for a kind of hyper-chaotic financial model. Since some important economic indexes are heavily related to region, the authors consider a nonlinear chaotic financial system with diffusion, which leads to some mathematical difficulties in dealing with the infinite-dimension characteristic. In order to overcome these difficulties, novel analysis techniques have to be proposed on the basis of Laplacian semigroup and impulsive control. Sufficient conditions are provided for existence and global exponential stabilization of positive solution for the system. It is interesting to discover that the impulse strength can be larger than 1 in the newly obtained stability criterion. Numerical simulations show the effectiveness of theoretical analysis.

Suggested Citation

  • Xinggui Li & Ruofeng Rao & Xinsong Yang, 2022. "Impulsive Stabilization on Hyper-Chaotic Financial System under Neumann Boundary," Mathematics, MDPI, vol. 10(11), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1866-:d:827704
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    References listed on IDEAS

    as
    1. Sun, Jitao, 2004. "Impulsive control of a new chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(6), pages 669-677.
    2. Quanyu Bai & Wei Zhu, 2022. "Event-Triggered Impulsive Optimal Control for Continuous-Time Dynamic Systems with Input Time-Delay," Mathematics, MDPI, vol. 10(2), pages 1-16, January.
    3. Yan Ji & Jinde Cao, 2022. "Parameter Estimation Algorithms for Hammerstein Finite Impulse Response Moving Average Systems Using the Data Filtering Theory," Mathematics, MDPI, vol. 10(3), pages 1-16, January.
    4. Mohammed Salah Abd-Elouahab & Nasr-Eddine Hamri & Junwei Wang, 2010. "Chaos Control of a Fractional-Order Financial System," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-18, July.
    5. Nazarimehr, Fahimeh & Sheikh, Javad & Ahmadi, Mohammad Mahdi & Pham, Viet–Thanh & Jafari, Sajad, 2018. "Fuzzy predictive controller for chaotic flows based on continuous signals," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 349-354.
    6. 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.
    7. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
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