The Self Interaction and Mutual Interaction of Limit Cycles

D. S. Broomhead
1980 Progress of theoretical physics  
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
more » ... 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.
doi:10.1143/ptp.63.1081 fatcat:fgxtet6a2nhurc2gn7bpqoltrm