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Impact of bounded noise and shortcuts on the spatiotemporal dynamics of neuronal networks

Author

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  • Yang, X.L.
  • Jia, Y.B.
  • Zhang, L.

Abstract

The influences of bounded noise together with shortcuts on the spatiotemporal collective behaviors of temporal coherence and spatial synchronization are discussed in neuronal networks. Firstly, we focus on the case of regular neuronal networks. With the increase of noise amplitude, we find that the spatial synchronizability among coupled neurons is always impaired and coherence resonance, however, occurs at an appropriately tuned level of noise amplitude. Then, we introduce shortcuts to the regular neuronal networks to formulate small-world neuronal networks. The results indicate that the spatial synchronization and temporal coherence in the networks can be enhanced with the addition of shortcuts. Moreover, we verify that there exists an optimal amount of added shortcuts such that the small-world networks reach much more ordered spatiotemporal patterns, i.e., coupled neurons are nearly synchronized in space and most coherent in time. In addition, the shortcuts-induced much more ordered states are confirmed to be robust against changes of the intensity of the unit Wiener process.

Suggested Citation

  • Yang, X.L. & Jia, Y.B. & Zhang, L., 2014. "Impact of bounded noise and shortcuts on the spatiotemporal dynamics of neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 617-623.
    • Handle: RePEc:eee:phsmap:v:393:y:2014:i:c:p:617-623
    DOI: 10.1016/j.physa.2013.09.021
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    Cited by:

    1. Yuangen Yao & Haiyou Deng & Chengzhang Ma & Ming Yi & Jun Ma, 2017. "Impact of Bounded Noise and Rewiring on the Formation and Instability of Spiral Waves in a Small-World Network of Hodgkin-Huxley Neurons," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-13, January.
    2. Cheng, Guanghui & Gui, Rong & Yao, Yuangen & Yi, Ming, 2019. "Enhancement of temporal regularity and degradation of spatial synchronization induced by cross-correlated sine-Wiener noises in regular and small-world neuronal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 361-369.
    3. Yuangen Yao & Lijian Yang & Canjun Wang & Quan Liu & Rong Gui & Juan Xiong & Ming Yi, 2018. "Subthreshold Periodic Signal Detection by Bounded Noise-Induced Resonance in the FitzHugh–Nagumo Neuron," Complexity, Hindawi, vol. 2018, pages 1-10, February.
    4. Yuangen Yao & Wei Cao & Qiming Pei & Chengzhang Ma & Ming Yi, 2018. "Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons," Complexity, Hindawi, vol. 2018, pages 1-10, April.

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