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The Positive Role of Multiplicative Noise in Complete Synchronization of Unidirectionally Coupled Ring with Three Nodes

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  • Yuzhu Xiao
  • Sufang Tang
  • Zhongkui Sun

Abstract

The role of multiplicative noise in the synchronization of unidirectionally coupled ring with three nodes is studied. Based on the theory of stochastic differential equations, we demonstrate that noise plays a positive role in complete synchronization. In numerical simulations, the Lorenz system, Rössler like system, and Hindmarsh‐Rose neuron model are employed to demonstrate the correctness of our theoretical result.

Suggested Citation

  • Yuzhu Xiao & Sufang Tang & Zhongkui Sun, 2014. "The Positive Role of Multiplicative Noise in Complete Synchronization of Unidirectionally Coupled Ring with Three Nodes," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:741961
    DOI: 10.1155/2014/741961
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    References listed on IDEAS

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    1. Xiuchun Li & Jianhua Gu & Wei Xu, 2013. "Adaptive Integral Observer-Based Synchronization for Chaotic Systems with Unknown Parameters and Disturbances," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, May.
    2. Xiuchun Li & Jianhua Gu & Wei Xu, 2013. "Adaptive Integral Observer‐Based Synchronization for Chaotic Systems with Unknown Parameters and Disturbances," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Giuseppe Pesce & Austin McDaniel & Scott Hottovy & Jan Wehr & Giovanni Volpe, 2013. "Stratonovich-to-Itô transition in noisy systems with multiplicative feedback," Nature Communications, Nature, vol. 4(1), pages 1-7, December.
    4. Wu, Ying & Xu, Jianxue & He, Daihai & Earn, David J.D., 2005. "Generalized synchronization induced by noise and parameter mismatching in Hindmarsh–Rose neurons," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1605-1611.
    5. Moreno Vega, Yamir & Vázquez-Prada, Miguel & F. Pacheco, Amalio, 2004. "Fitness for synchronization of network motifs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 279-287.
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    Cited by:

    1. Zhang, Ruoqi & Lin, Lifeng & Wang, Huiqi, 2025. "Synchronization resilience of coupled fluctuating-damping oscillators in small-world weighted complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).

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