A method is described for the derivation of dissipative models from Hamiltonian systems in such a way that the global behaviour remains intuitively clear. Using this approach a model is constructed in which an attracting limit cycle can interact with itself and break into two smaller limit cycles. The structural instability near such a bifurcation is demonstrated. Thus it is shown that complicated motion characterized by the existence of homoclinic points may be found as a result of small

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... ic extrinsic or intrinsic perturbations. Finally a comment is made on the possible relevance of this kind of instability to recent work on the Belousov-Zhabotinskii reaction.