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Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control

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  • Li Xu
  • Ruiwen Han

Abstract

In this paper, a discrete space-time Lotka–Volterra model with the periodic boundary conditions and feedback control is proposed. By means of a discrete version of comparison theorem, the boundedness of the nonnegative solution of the system is proved. By the combination of the Volterra-type and quadratic Lyapunov functions, the global asymptomatic stability of the unique positive equilibrium is investigated. Finally, numerical simulations are presented to verify the effectiveness of the main results.

Suggested Citation

  • Li Xu & Ruiwen Han, 2020. "Global Stability for a Discrete Space-Time Lotka–Volterra System with Feedback Control," Complexity, Hindawi, vol. 2020, pages 1-9, August.
    • Handle: RePEc:hin:complx:2960503
    DOI: 10.1155/2020/2960503
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    Cited by:

    1. Gao, Shang & Peng, Keyu & Zhang, Chunrui, 2021. "Existence and global exponential stability of periodic solutions for feedback control complex dynamical networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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