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Stability and Hopf bifurcation analysis for a two-species commensalism system with delay. (English) Zbl 1481.34096

Summary: 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.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34K13 Periodic solutions to functional-differential equations
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
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