Direct computation of period doubling bifurcation points of large-scale systems of ODEs using a Newton-Picard method

1999 ◽  
Vol 19 (4) ◽  
pp. 525-547 ◽  
Author(s):  
K Engelborghs
Keyword(s):  
Large Scale ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Direct Computation ◽  
Large Scale Systems ◽  
Bifurcation Points ◽  
Systems Of Odes ◽  
Picard Method

SPATIAL INTERMITTENCY IN AN INHOMOGENEOUS COUPLED MAP LATTICE

2002 ◽  
Vol 12 (06) ◽  
pp. 1363-1370 ◽  
Author(s):  
ASHUTOSH SHARMA ◽  
NEELIMA GUPTE
Keyword(s):  
Power Law ◽  
Length Distribution ◽  
Period Doubling ◽  
Linear Analysis ◽  
Coupled Map Lattice ◽  
Period Doubling Bifurcation ◽  
Scaling Exponent ◽  
Power Law Distribution ◽  
Periodic Behavior ◽  
Bifurcation Points

We observe purely spatial intermittency accompanied by temporally periodic behavior in an inhomogeneous lattice of coupled logistic maps where the inhomogenity appears in the form of different values of the map parameters at distinct sites. Linear analysis shows that the spatial intermittency appears in the neighborhood of tangent period doubling bifurcation points. The intermittency near the bifurcation points is associated with a power-law distribution for the laminar lengths. The scaling exponent ζ for the laminar length distribution is obtained.

SINGULAR POINTS OF PLANE CURVES GENERATED BY PERIOD DOUBLING BIFURCATION POINTS AND A METHOD FOR COMPUTING THEM

1991 ◽  
Vol 01 (04) ◽  
pp. 795-802 ◽  
Author(s):  
NORIO YAMAMOTO
Keyword(s):  
Nonlinear Oscillations ◽  
Period Doubling ◽  
Singular Points ◽  
Period Doubling Bifurcation ◽  
Plane Curves ◽  
Bifurcation Equation ◽  
Dimensional Parameter ◽  
Bifurcation Points ◽  
Isolated Points ◽  
Cusp Points

This paper is concerned with nodal points, isolated points and cusp points (PD) appearing on a locus of period-doubling bifurcation points and the accurate location of them. Such points can be observed in periodic differential systems (e.g., Duffing's equation) in nonlinear oscillations. In a suitable two-dimensional parameter-plane, such points can be formulated as double (singular) points of plane curves defined by a bifurcation equation, and a method for computing them is proposed.

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