Example of a blue sky catastrophe

American Mathematical Society Translations: Series 2 - Methods of Qualitative Theory of Differential Equations and Related Topics ◽

10.1090/trans2/200/09 ◽

2000 ◽

pp. 99-105 ◽

Cited By ~ 6

Author(s):

Nikolaĭ Gavrilov ◽

Andrey Shilnikov

Keyword(s):

Blue Sky Catastrophe

Download Full-text

Stochastic oscillations near the “blue sky catastrophe” bifurcation in neuron model

10.1063/1.5055155 ◽

2018 ◽

Author(s):

Lev Ryashko ◽

Evdokia Slepukhina

Keyword(s):

Neuron Model ◽

Blue Sky Catastrophe ◽

Stochastic Oscillations

Download Full-text

Triple mode alignment in a canonical model of the blue-sky catastrophe

Nonlinear Dynamics ◽

10.1007/s11071-013-0794-y ◽

2013 ◽

Vol 73 (1-2) ◽

pp. 397-403 ◽

Cited By ~ 11

Author(s):

Robert A. Van Gorder

Keyword(s):

Canonical Model ◽

Blue Sky Catastrophe ◽

Triple Mode

Download Full-text

Cascade of bifurcations in Lorenz-like systems: Birth of a strange attractor, blue sky catastrophe bifurcation, and nine homoclinic bifurcations

Doklady Mathematics ◽

10.1134/s106456241505018x ◽

2015 ◽

Vol 92 (2) ◽

pp. 563-567 ◽

Cited By ~ 4

Author(s):

G. A. Leonov

Keyword(s):

Strange Attractor ◽

Homoclinic Bifurcations ◽

Blue Sky Catastrophe

Download Full-text

Transition between Tonic Spiking and Bursting in a Neuron Model via the Blue-Sky Catastrophe

Physical Review Letters ◽

10.1103/physrevlett.94.048101 ◽

2005 ◽

Vol 94 (4) ◽

Cited By ~ 115

Author(s):

Andrey Shilnikov ◽

Gennady Cymbalyuk

Keyword(s):

Neuron Model ◽

Blue Sky Catastrophe

Download Full-text

The bifurcation of the ?blue sky catastrophe? on two-dimensional manifolds

Mathematical Notes ◽

10.1007/bf01229439 ◽

1992 ◽

Vol 51 (1) ◽

pp. 76-81 ◽

Cited By ~ 2

Author(s):

V. S. Medvedev

Keyword(s):

Two Dimensional ◽

Blue Sky Catastrophe

Download Full-text

Blue sky catastrophe in relaxation systems with one fast and two slow variables

Differential Equations ◽

10.1134/s0012266108020031 ◽

2008 ◽

Vol 44 (2) ◽

pp. 161-175 ◽

Cited By ~ 10

Author(s):

S. D. Glyzin ◽

A. Yu. Kolesov ◽

N. Kh. Rozov

Keyword(s):

Relaxation Systems ◽

Blue Sky Catastrophe ◽

Slow Variables

Download Full-text

Blue-Sky Catastrophe in Singularly Perturbed Systems

Moscow Mathematical Journal ◽

10.17323/1609-4514-2005-5-1-269-282 ◽

2005 ◽

Vol 5 (1) ◽

pp. 269-282 ◽

Cited By ~ 26

Author(s):

A. Shilnikov ◽

L. Shilnikov ◽

D. Turaev

Keyword(s):

Singularly Perturbed ◽

Singularly Perturbed Systems ◽

Perturbed Systems ◽

Blue Sky Catastrophe

Download Full-text

A fuzzy blue sky catastrophe

Nonlinear Science and Complexity ◽

10.1142/9789812772428_0012 ◽

2006 ◽

Author(s):

Ling Hong ◽

J. Q. Sun

Keyword(s):

Blue Sky Catastrophe

Download Full-text

Bifurcation of Homoclinic Orbits in Autonomous Systems and in Chaotic Blue Sky Catastrophe

IUTAM Symposium on New Applications of Nonlinear and Chaotic Dynamics in Mechanics - Solid Mechanics and its Applications ◽

10.1007/978-94-011-5320-1_10 ◽

1999 ◽

pp. 93-100

Author(s):

M. Belhaq ◽

F. Lakrad

Keyword(s):

Autonomous Systems ◽

Homoclinic Orbits ◽

Blue Sky Catastrophe

Download Full-text

Blue sky catastrophe as applied to modeling of cardiac rhythms

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542515070076 ◽

2015 ◽

Vol 55 (7) ◽

pp. 1120-1137 ◽

Cited By ~ 2

Author(s):

S. D. Glyzin ◽

A. Yu. Kolesov ◽

N. Kh. Rozov

Keyword(s):

Blue Sky Catastrophe

Download Full-text