Transient periodic behaviour related to a saddle-node bifurcation


Damme, Ruud van and Valkering, Theo P. (1987) Transient periodic behaviour related to a saddle-node bifurcation. Journal of Physics A: Mathematical and general, 20 (13). p. 4161. ISSN 0305-4470

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Abstract:The authors investigate transient periodic orbits of dissipative invertible maps of R2. Such orbits exist just before, in parameter space, a saddle-node pair is formed. They obtain numerically and analytically simple scaling laws for the duration of the transient, and for the region of initial conditions which evolve into transient periodic orbits. An estimate of this region is then obtained by the construction-after extension of the map to C2-of the stable manifolds of the two complex saddles in C2 that bifurcate ino the real saddle-node pair
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Copyright:© 1987 Institute of Physics
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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