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- Title
Necessary and sufficient conditions of the existence of homoclinic trajectories and cascade of bifurcations in Lorenz-like systems: birth of strange attractor and 9 homoclinic bifurcations.
- Authors
Leonov, G.
- Abstract
Necessary and sufficient conditions of the existence of homoclinic trajectories in Lorenz-like systems are obtained. The Shimizu-Morioka, Lu, and Chen systems are considered. For special Lorenz-like system with zero saddle value, cascade of bifurcations is obtained. Birth of strange attractor, blue sky catastrophe and 9 homoclinic bifurcations are discovered.
- Subjects
LORENZ equations; TRAJECTORY measurements; BIFURCATION theory; ATTRACTORS (Mathematics); NONLINEAR dynamical systems
- Publication
Nonlinear Dynamics, 2016, Vol 84, Issue 2, p1055
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-015-2549-4