Global bifurcations and homoclinic chaos in nonlinear panel optomechanical resonators under combined thermal and radiation stresses

2020 ◽  
Author(s):  
E. Hollander ◽  
O. Gottlieb
Keyword(s):  
Global Bifurcations ◽  
Homoclinic Chaos

Investigation of Global Bifurcations in Planar Vector Fields

1988 ◽  
Author(s):  
John Guckenheimer
Keyword(s):  
Vector Fields ◽  
Global Bifurcations ◽  
Planar Vector Fields ◽  
Planar Vector

Local and global bifurcations in 3D piecewise smooth discontinuous maps

2021 ◽  
Vol 31 (1) ◽  
pp. 013126
Author(s):  
Mahashweta Patra ◽  
Sayan Gupta ◽  
Soumitro Banerjee
Keyword(s):  
Piecewise Smooth ◽  
Global Bifurcations ◽  
Local And Global Bifurcations

Nontransversal curves of T-points: a source of closed curves of global bifurcations

2002 ◽  
Vol 303 (2-3) ◽  
pp. 204-211 ◽  
Author(s):  
A. Algaba ◽  
F. Fernández-Sánchez ◽  
E. Freire ◽  
M. Merino ◽  
A.J. Rodrı́guez-Luis
Keyword(s):  
Global Bifurcations ◽  
Closed Curves

Homoclinic chaos in strongly dissipative strongly coupled complex dusty plasmas

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Samiran Ghosh
Keyword(s):  
Dusty Plasmas ◽  
Strongly Coupled ◽  
Homoclinic Chaos

Global bifurcations in externally excited autoparametric systems

2010 ◽  
Vol 45 (8) ◽  
pp. 766-792 ◽  
Author(s):  
Hongkui Chen ◽  
Qingyu Xu
Keyword(s):  
Global Bifurcations

Experimental evidence for homoclinic chaos in the Belousov-Zhabotinskii reaction

1987 ◽  
Vol 120 (6) ◽  
pp. 269-275 ◽  
Author(s):  
F. Argoul ◽  
A. Arneodo ◽  
P. Richetti
Keyword(s):  
Experimental Evidence ◽  
Homoclinic Chaos ◽  
Belousov Zhabotinskii Reaction

LOCAL AND GLOBAL BIFURCATIONS IN THREE-DIMENSIONAL, CONTINUOUS, PIECEWISE SMOOTH MAPS

2011 ◽  
Vol 21 (06) ◽  
pp. 1617-1636 ◽  
Author(s):  
SOMA DE ◽  
PARTHA SHARATHI DUTTA ◽  
SOUMITRO BANERJEE ◽  
AKHIL RANJAN ROY
Keyword(s):  
Three Dimensional ◽  
Global Bifurcation ◽  
Period Doubling ◽  
Piecewise Smooth ◽  
Numerical Continuation ◽  
Homoclinic Tangency ◽  
Global Dynamics ◽  
Global Bifurcations ◽  
Border Collision Bifurcation ◽  
Smooth Map

In this work, we study the dynamics of a three-dimensional, continuous, piecewise smooth map. Much of the nontrivial dynamics of this map occur when its fixed point or periodic orbit hits the switching manifold resulting in the so-called border collision bifurcation. We study the local and global bifurcation phenomena resulting from such borderline collisions. The conditions for the occurrence of nonsmooth period-doubling, saddle-node, and Neimark–Sacker bifurcations are derived. We show that dangerous border collision bifurcation can also occur in this map. Global bifurcations arise in connection with the occurrence of nonsmooth Neimark–Sacker bifurcation by which a spiral attractor turns into a saddle focus. The global dynamics are systematically explored through the computation of resonance tongues and numerical continuation of mode-locked invariant circles. We demonstrate the transition to chaos through the breakdown of mode-locked torus by degenerate period-doubling bifurcation, homoclinic tangency, etc. We show that in this map a mode-locked torus can be transformed into a quasiperiodic torus if there is no global bifurcation.

Global Dynamics in the Leslie–Gower Model with the Allee Effect

2018 ◽  
Vol 28 (12) ◽  
pp. 1850151 ◽  
Author(s):  
Valery A. Gaiko ◽  
Cornelis Vuik
Keyword(s):  
Singular Point ◽  
Bifurcation Analysis ◽  
Limit Cycles ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Global Dynamics ◽  
Global Bifurcations ◽  
Biomedical System

We complete the global bifurcation analysis of the Leslie–Gower system with the Allee effect which models the dynamics of the populations of predators and their prey in a given ecological or biomedical system. In particular, studying global bifurcations of limit cycles, we prove that such a system can have at most two limit cycles surrounding one singular point.

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