scholarly journals Parametric normal forms for Bogdanov--Takens singularity; the generalized saddle-node case

2015 ◽  
Vol 35 (1) ◽  
pp. 205-224 ◽  
Author(s):  
Majid Gazor ◽  
◽  
Mojtaba Moazeni
Keyword(s):  
Normal Forms ◽  
Saddle Node ◽  
Parametric Normal Forms

FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS

2010 ◽  
Vol 20 (11) ◽  
pp. 3487-3515 ◽  
Author(s):  
MAJID GAZOR ◽  
PEI YU
Keyword(s):  
Dynamical Systems ◽  
Normal Form ◽  
Decomposition Method ◽  
Normal Forms ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Multiple Parameters ◽  
Formal Basis ◽  
Parametric Normal Forms ◽  
Parametric Systems

We introduce a formal decomposition method for efficiently computing the parametric normal form of nonlinear dynamical systems with multiple parameters. Recently introduced notions of formal basis style and costyle are applied through formal decomposition method to obtain the simplest parametric normal form for degenerate nonlinear parametric center. The necessary formulas are derived and implemented using Maple to compute the simplest parametric normal form of degenerate and nondegenerate nonlinear centers. Our program computes the order of any planar parametric systems associated with this singularity.

scholarly journals Analytic normal forms for convergent saddle-node vector fields

2015 ◽  
Vol 65 (3) ◽  
pp. 933-974 ◽  
Author(s):  
Reinhard Schäfke ◽  
Loïc Teyssier
Keyword(s):  
Vector Fields ◽  
Normal Forms ◽  
Saddle Node

GEOMETRY AND ORDER OF CHAOS

1999 ◽  
Vol 09 (02) ◽  
pp. 327-347
Author(s):  
J. AWREJCEWICZ ◽  
C.-H. LAMARQUE ◽  
K. A. BROUGHAN
Keyword(s):  
Normal Forms ◽  
High Order ◽  
Chaotic Attractors ◽  
Geometrical Structures ◽  
Saddle Node Bifurcation ◽  
Geometrical Properties ◽  
Saddle Node ◽  
Fractal Organization ◽  
In The Beginning

In the beginning a brief introduction to a symmetry increasing as well as to quantified geometrical structures of chaotic attractors have been given. Then, the research is focused on the Chossat–Golubitsky map. A saddle-node bifurcation on the boundary of the umbrella shape set of saddles, crises of two peculiar structures of saddles and an extremely high order of infinitely many flip and regular saddle orbits have been reported. The geometrical properties of hyperchaos and its relation to the Kakeya–Besicovitch and the Apollonian packing have been illustrated and discussed. A fractal organization of the successive periodic saddles and fractal normal forms have been described.

Attractor-preserving control to avoid saddle-node bifurcation

2014 ◽  
Vol 2 ◽  
pp. 150-153
Author(s):  
Daisuke Ito ◽  
Tetsushi Ueta ◽  
Shigeki Tsuji ◽  
Kazuyuki Aihara
Keyword(s):  
Saddle Node Bifurcation ◽  
Saddle Node

METHODS OF REDUCING OF LARGE BOOLEAN FORMULAS REPRESENTED IN A CONJUNCTIVE NORMAL FORM FOR DETERMINING THEIR SATISFIABILITY

2020 ◽  
Author(s):  
N.I. Gdansky ◽  
◽  
A.A. Denisov ◽  
Keyword(s):  
Normal Form ◽  
Normal Forms ◽  
Conjunctive Normal Form ◽  
Boolean Formulas

The article explores the satisfiability of conjunctive normal forms used in modeling systems.The problems of CNF preprocessing are considered.The analysis of particular methods for reducing this formulas, which have polynomial input complexity is given.

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