TWO TYPES OF HOPF BIFURCATION POINTS: SOURCES AND SINKS OF FAMILIES OF PERIODIC ORBITS*

1980 ◽  
Vol 357 (1) ◽  
pp. 300-304 ◽  
Author(s):  
John Mallet-Paret ◽  
James A. Yorke
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Orbits ◽  
Sources And Sinks ◽  
Bifurcation Points ◽  
Families Of Periodic Orbits

DYNAMICS AND DOUBLE HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY

2009 ◽  
Vol 19 (11) ◽  
pp. 3733-3751 ◽  
Author(s):  
SUQI MA ◽  
ZHAOSHENG FENG ◽  
QISHAI LU
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Center Manifold ◽  
Hopf Bifurcations ◽  
Value Of Time ◽  
Asymptotically Stable ◽  
Universal Unfolding ◽  
Double Hopf Bifurcation ◽  
Bifurcation Points ◽  
The Rose

In this paper, we are concerned with the Rose–Hindmarsh model with time delay. By applying the generalized Sturm criterion, a number of imaginary roots of the characteristic equation are classified. The absolutely stable regions for any value of time delay are detected. By the continuous software DDE-Biftool, both the Hopf bifurcation curves and double Hopf bifurcation points are illustrated in parametric spaces. The normal form and universal unfolding at double Hopf bifurcation points are considered by the center manifold method. Some examples also indicate that the corresponding unique attractor near each double Hopf point is asymptotically stable.

Families of Periodic Orbits for Solar Sails in the CRBTP

2014 ◽  
pp. 871-884 ◽  
Author(s):  
Patricia Verrier ◽  
Thomas Waters ◽  
Jan Sieber
Keyword(s):  
Periodic Orbits ◽  
Solar Sails ◽  
Families Of Periodic Orbits

Optimal control of nonlinear aeroelastic system with non‐semi‐simple eigenvalues at Hopf bifurcation points

2020 ◽  
Vol 41 (5) ◽  
pp. 1524-1542
Author(s):  
Licai Wang ◽  
Yudong Chen ◽  
Chunyan Pei ◽  
Lina Liu ◽  
Suhuan Chen
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Aeroelastic System ◽  
Bifurcation Points
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