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Global existence of periodic solutions in the linearly coupled Mackey-Glass system. (English) Zbl 1215.34080

Summary: The dynamics of a linearly coupled Mackey-Glass system with delay are investigated. Based on the distribution of eigenvalues, we prove that a sequence of Hopf bifurcation occurs at the positive equilibrium as the delay increases and obtain the bifurcation set in the parameter plane. The explicit algorithm for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived, using the theories of normal form and center manifold. The global existence of periodic solutions is established using a global Hopf bifurcation result.

MSC:

34K13 Periodic solutions to functional-differential equations
34K18 Bifurcation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
34K17 Transformation and reduction of functional-differential equations and systems, normal forms
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