Bifurcations for Goodwin model with three delays

In this paper, the Goodwin model with three delays is investigated. By choosing the sum $$\tau $$τ of three delays as a bifurcation parameter, we show that Hopf bifurcations can occur as $$\tau $$τ crosses some critical values. By deriving the equation describing the flow on the center manifold, we can determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. In addition, special attention is paid to the global continuation of local Hopf bifurcations. Finally, several numerical simulations supporting the theoretical analysis are also given.

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