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Bifurcation analysis and \(\pmb {H_{\infty }}\) control of a stochastic competition model with time delay and harvesting

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Abstract

In this paper, a stochastic competition model with time delay and harvesting is investigated. By means of the stochastic center manifold reduction principle and stochastic averaging method, the model is simplified to a one-dimensional Markov diffusing process. The singular boundary theory and invariant measure are applied in analyzing the stochastic stability and bifurcation. The T-S fuzzy model of the system is constructed, and the \(H_{\infty }\) state feedback controller is designed to eliminate the instability phenomenon by using a linear matrix inequality approach. Finally, numerical simulations are given to demonstrate our results.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Funding

This study was funded by the National Natural Science Foundation of China (61703083 and 61673100), China Scholarship Council (201706085041) and Fundamental Research Funds for the Central Universities (N2104007).

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Correspondence to Yue Zhang.

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Zhang, Y., Zhang, J. & Liu, X. Bifurcation analysis and \(\pmb {H_{\infty }}\) control of a stochastic competition model with time delay and harvesting. Nonlinear Dyn 109, 1217–1232 (2022). https://doi.org/10.1007/s11071-022-07381-y

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