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

作者：Leonov G A^*

来源：Nonlinear Dynamics, 2016, 84(2): 1055-1062.

DOI：10.1007/s11071-015-2549-4

• Homoclinic trajectories
• Strange attractor
• Blue sky catastrophe
• Cascade of bifurcations
• Fishing principle
• Lorenz-like system
• Chen system
• Lu system
• Shimizu-Morioka system
• Saddle value
• Separatrix of saddle point

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.

• 出版日期2016-4