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Stability and Hopf Bifurcation Analysis for a Two-Species Commensalism System with Delay

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Abstract

This paper is devoted to studying the dynamics of a two-species commensalism system with delay. By analyzing the characteristic equation and regarding the time delay as the bifurcation parameter, we investigate the local asymptotic stability of the positive equilibrium and show the existence of periodic solutions bifurcating from the positive equilibrium. Then, we derive the precise formulae to determine the Hopf bifurcation direction and the stability of the bifurcating periodic solutions by using the normal form theory and the center manifold theorem. Numerical simulation results are also included to support our theoretical analysis.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 12071491). We are grateful to the editors and reviewers for helpful comments and suggestions.

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  1. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, Guangdong, People’s Republic of China

    Tianyang Li & Qiru Wang

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  1. Tianyang Li
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  2. Qiru Wang
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Correspondence to Qiru Wang.

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This research was supported by the National Natural Science Foundation of China (No. 12071491)

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Li, T., Wang, Q. Stability and Hopf Bifurcation Analysis for a Two-Species Commensalism System with Delay. Qual. Theory Dyn. Syst. 20, 83 (2021). https://doi.org/10.1007/s12346-021-00524-3

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