TY - JOUR
T1 - Bifurcations of an optically pumped three-level laser model
AU - Forysiak, W.
AU - Moloney, J. V.
AU - Harrison, R. G.
N1 - Funding Information:
The authors acknowledget he SERC (UK) for support of this work and also partial support under the auspiceso f a European Twinning Contract (X1*0325-C @MA)).
PY - 1991/10
Y1 - 1991/10
N2 - We study the bifurcations in a sixth-order model of a resonant, homogeneously broadened, three-level, optically pumped laser. Standard analytical and numerical techniques are used to obtain a complete unfolding of the model's equilibrium bifurcations in its four-dimensional parameter space. Regions of stationary, periodic and potentially chaotic behaviour are then readily identified. Turning to two specific cases, we study the principal global bifurcations in a two-parameter plane and show their origin in special degenerate bifurcation points of codimension two. The different relative dispositions of the principal homoclinic and heteroclinic connections in these two examples result in different local bifurcation behaviours and chaotic dynamics, which we illustrate in detail.
AB - We study the bifurcations in a sixth-order model of a resonant, homogeneously broadened, three-level, optically pumped laser. Standard analytical and numerical techniques are used to obtain a complete unfolding of the model's equilibrium bifurcations in its four-dimensional parameter space. Regions of stationary, periodic and potentially chaotic behaviour are then readily identified. Turning to two specific cases, we study the principal global bifurcations in a two-parameter plane and show their origin in special degenerate bifurcation points of codimension two. The different relative dispositions of the principal homoclinic and heteroclinic connections in these two examples result in different local bifurcation behaviours and chaotic dynamics, which we illustrate in detail.
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U2 - 10.1016/0167-2789(91)90170-E
DO - 10.1016/0167-2789(91)90170-E
M3 - Article
AN - SCOPUS:0000496566
SN - 0167-2789
VL - 53
SP - 162
EP - 186
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1
ER -