Abstract
The homoclinic and heteroclinic intersections of the stable and unstable manifolds of the fixed and periodic points in the Poincaré maps of the periodically forced Brusselator have been studied by direct integration of the system using periodic-orbit following technique. Since the free limit cycle oscillator does not possess any saddle points where one may start the construction of invariant manifolds, one has to look into the Poincaré sections in the extended phase space with the time axis included. We have followed a series of homoclinic and heteroclinic crossings and the one-piece chaotic attractor appears to be the envelope of unstable manifolds of all orders.
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