, Volume 6, Issue 1, pp 147-173

Heteroclinic orbits in singular systems: A unifying approach

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Abstract

We consider singularly perturbed systems \(\xi = f(\xi ,\eta ,\varepsilon ),\dot \eta = \varepsilon g(\xi ,\eta ,\varepsilon )\) , such thatξ=f(ξ, αo, 0). αo∃ℝ m , has a heteroclinic orbitu(t). We construct a bifurcation functionG(α, ɛ) such that the singular system has a heteroclinic orbit if and only ifG(α, ɛ)=0 has a solutionα=α(ɛ). We also apply this result to recover some theorems that have been proved using different approaches.