Local and global bifurcation in periodic scalar ODEs Original Research Article

Following the lines of Yu. Ilyashenko and W. Li, we propose a definition of local and global bifurcations for the family of differential equations x′=f(t,x,λ)x′=f(t,x,λ), where f∈C(R3)f∈C(R3) is locally Lipschitz continuous with respect to xx, and TT-periodic in tt. Then, we prove that a value of the parameter λλ is a global bifurcation value if and only if there exists a local bifurcation point (including bifurcation points at infinity) for this value of the parameter.