scholarly journals Dynamical playground of a higher-order cubic Ginzburg-Landau equation: From orbital connections and limit cycles to invariant tori and the onset of chaos

2016 ◽  
Vol 94 (1) ◽  
Author(s):  
V. Achilleos ◽  
A. R. Bishop ◽  
S. Diamantidis ◽  
D. J. Frantzeskakis ◽  
T. P. Horikis ◽  
...  
Keyword(s):  
Limit Cycles ◽  
Landau Equation ◽  
Invariant Tori ◽  
Higher Order ◽  
Ginzburg Landau ◽  
Onset Of Chaos ◽  
Ginzburg Landau Equation

Onset of chaos in the generalized Ginzburg-Landau equation

1990 ◽  
Vol 42 (10) ◽  
pp. 6238-6240 ◽  
Author(s):  
Boris A. Malomed ◽  
Alexander A. Nepomnyashchy
Keyword(s):  
Landau Equation ◽  
Ginzburg Landau ◽  
Onset Of Chaos ◽  
Ginzburg Landau Equation

Onset of chaos in the weakly dissipative two-dimensional complex Ginzburg-Landau equation

1996 ◽  
Vol T67 ◽  
pp. 143-147 ◽  
Author(s):  
Michael A Zaks ◽  
Alexander A Nepomnyashchy ◽  
Boris A Malomed
Keyword(s):  
Landau Equation ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Onset Of Chaos ◽  
Ginzburg Landau Equation

scholarly journals Transition from non-periodic to periodic explosions

2015 ◽  
Vol 373 (2056) ◽  
pp. 20150114 ◽  
Author(s):  
Carlos Cartes ◽  
Orazio Descalzi
Keyword(s):  
Transmission Lines ◽  
Landau Equation ◽  
Period Doubling ◽  
Higher Order ◽  
Ginzburg Landau ◽  
Equation Modelling ◽  
Ginzburg Landau Equation ◽  
Dissipative Solitons ◽  
Soliton Transmission ◽  
Period Doubling Bifurcations

We show the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order nonlinear and dispersive effects are added to the complex cubic–quintic Ginzburg–Landau equation modelling soliton transmission lines. This counterintuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations (or intermittency) leading to chaos (non-periodic explosions).

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