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Stability analysis for stochastic complex-valued delayed networks with multiple nonlinear links and impulsive effects

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Abstract

This paper focuses on the stability of stochastic complex-valued delayed networks with multiple nonlinear links and impulsive effects. Different from the previous work, the links among nodes are multiple and can be nonlinear. Besides, the features of complex variables, time-varying delays and stochastic perturbations are taken into account. By utilizing complex version Itô’s formula, impulsive differential inequalities with multiple delays and graph-theoretical technique, several stability criteria are given without splitting the real and imaginary parts. These stability criteria show that if the impulsive dynamics is stable while continuous dynamics is not, it requires the dwell time of impulsive sequences to be small. Conversely, if the continuous dynamics is stable while impulsive dynamics is not, it requires the dwell time of impulsive sequences to be large. Then the theoretical results are applied to a class of stochastic complex-valued coupled oscillators. The numerical examples are carried out for demonstration purpose.

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Acknowledgements

This work was supported by the NNSF of China (Nos. 11671072, 61773137); Shandong Province Natural Science Foundation (Nos. ZR2018MA005, ZR2018MA020, ZR2017MA008); the Key Project of Science and Technology of Weihai (No. 2014DXGJMS08) and the Innovation Technology Funding Project in Harbin Institute of Technology (No. HIT.NSRIF.201703).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology (Weihai), 264209, Weihai, People’s Republic of China

    Pengfei Wang & Huan Su

  2. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Zhenyao Sun & Meng Fan

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  1. Pengfei Wang
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Correspondence to Huan Su.

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Wang, P., Sun, Z., Fan, M. et al. Stability analysis for stochastic complex-valued delayed networks with multiple nonlinear links and impulsive effects. Nonlinear Dyn 97, 1959–1976 (2019). https://doi.org/10.1007/s11071-019-04888-9

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