COMPLEXITY OF HOMOCLINIC BIFURCATIONS AND Ω-MODULI

1996 ◽  
Vol 06 (06) ◽  
pp. 969-989 ◽  
Author(s):  
S. V. GONCHENKO ◽  
O. V. STEN’KIN ◽  
D. V. TURAEV
Keyword(s):  
Parameter Analysis ◽  
Homoclinic Tangency ◽  
Topological Conjugacy ◽  
Two Dimensional ◽  
Control Parameters ◽  
Homoclinic Bifurcations ◽  
Complete Study ◽  
Splitting Parameter ◽  
Two Parameter ◽  
Nonwandering Set

Bifurcations of two-dimensional diffeomorphisms with a homoclinic tangency are studied in one-and two-parameter families. Due to the well-known impossibility of a complete study of such bifurcations, the problem is restricted to the study of the bifurcations of the so-called low-round periodic orbits. In this connection, the idea of taking Ω-moduli (continuous invariants of the topological conjugacy on the nonwandering set) as the main control parameters (together with the standard splitting parameter) is proposed. In this way, new bifurcational effects are found which do not occur at a one-parameter analysis. In particular, the density of cusp-bifurcations is revealed.

scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

Global Hydroelastic Analysis of Pontoon-Type VLFS

2009 ◽  
Author(s):  
L. L. Jiao ◽  
M. Greco ◽  
O. M. Faltinsen
Keyword(s):  
Numerical Solutions ◽  
Parameter Analysis ◽  
Local Analysis ◽  
Two Dimensional ◽  
Numerical Wave Tank ◽  
Regular Waves ◽  
Hydroelastic Analysis ◽  
Air Cushion ◽  
Numerical Wave ◽  
Hydroelastic Response

A two-dimensional composite strategy given by Greco et al. [1] is applied to couple a linear global solution with a nonlinear local analysis. Globally a linear hydroelastic analysis is performed by an accurate Beam-On-Elastic-Foundation (BOEF) method. A parameter analysis of hydroelastic response of the structure is also carried out. Locally, a two-dimensional fully-nonlinear numerical wave tank (NWT) in combination with a Boundary Element Method (BEM) is developed to estimate the interaction between regular waves and the structure restrained from rigid and elastic motions. The effect of air cushion is considered. Present results are compared with experimental data and other numerical solutions.

scholarly journals Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents

2009 ◽  
Vol 2009 ◽  
pp. 1-22 ◽  
Author(s):  
Edson D. Leonel
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Scaling Laws ◽  
Scaling Function ◽  
Initial Conditions ◽  
Invariant Tori ◽  
Dynamical Variable ◽  
Two Dimensional ◽  
Control Parameters ◽  
Average Value

A phase transition from integrability to nonintegrability in two-dimensional Hamiltonian mappings is described and characterized in terms of scaling arguments. The mappings considered produce a mixed structure in the phase space in the sense that, depending on the combination of the control parameters and initial conditions, KAM islands which are surrounded by chaotic seas that are limited by invariant tori are observed. Some dynamical properties for the largest component of the chaotic sea are obtained and described in terms of the control parameters. The average value and the deviation of the average value for chaotic components of a dynamical variable are described in terms of scaling laws, therefore critical exponents characterizing a scaling function that describes a phase transition are obtained and then classes of universality are characterized. The three models considered are: The Fermi-Ulam accelerator model, a periodically corrugate waveguide, and variant of the standard nontwist map.

RESONANT GLUING BIFURCATIONS

2000 ◽  
Vol 10 (09) ◽  
pp. 2141-2160 ◽  
Author(s):  
ROBERT W. GHRIST
Keyword(s):  
Saddle Point ◽  
Parameter Space ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Centre Manifold ◽  
Principal Eigenvalues ◽  
Homoclinic Connections ◽  
Homoclinic Bifurcations ◽  
Zero Entropy

We consider the codimension-three phenomenon of homoclinic bifurcations of flows containing a pair of orbits homoclinic to a saddle point whose principal eigenvalues are in resonance. We concentrate upon the simplest possible configuration, the so-called "figure-of-eight," and reduce the dynamics near the homoclinic connections to those on a two-dimensional locally invariant centre manifold. The ensuing resonant gluing bifurcations exhibit features of both gluing bifurcations and resonant homoclinic bifurcations. Under certain twist conditions, the bifurcation structure is extremely rich, although describing zero-entropy flows. The analysis carefully exploits the topology of the orbits, the centre manifold and the parameter space.

Similarity Solution for the Curved Two-Dimensional Jet

1972 ◽  
Vol 39 (4) ◽  
pp. 879-882
Author(s):  
G. K. Fleming ◽  
S. A. Alpay
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Nonlinear Equation ◽  
Similarity Solution ◽  
Separation Bubble ◽  
The Other ◽  
Wall Jet ◽  
Two Dimensional ◽  
Two Parameter ◽  
Outer Half

A similarity solution has been obtained for a fluid jet bounded on one side by a separation bubble and on the other by an unbounded region containing the same fluid. The inner boundary has been approximated by a porous pseudowall. The resulting mathematical model reduces to other cases such as the plane wall jet and the free curved jet. A two-parameter family of solutions to the resulting nonlinear equation for the outer half of the jet correlates well with experimental data.

scholarly journals To switch or not to switch – a machine learning approach for ferroelectricity

2020 ◽  
Vol 2 (5) ◽  
pp. 2063-2072 ◽  
Author(s):  
Sabine M. Neumayer ◽  
Stephen Jesse ◽  
Gabriel Velarde ◽  
Andrei L. Kholkin ◽  
Ivan Kravchenko ◽  
...  
Keyword(s):  
Machine Learning ◽  
Measured Signal ◽  
Learning Approach ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Machine Learning Methods ◽  
Machine Learning Approach ◽  
Signal Dependence ◽  
Two Parameter

The introduced two-dimensional representation of two-parameter signal dependence allows for clear interpretation and classification of the measured signal upon using machine learning methods.

On the Parameter Plane of Nonlinear Coupled Oscillators

1993 ◽  
Vol 48 (5-6) ◽  
pp. 655-662
Author(s):  
Wolfgang Metzler ◽  
Achim Brelle ◽  
Klaus-Dieter Schmidt ◽  
Gerrit Danker ◽  
Matthias Köppe ◽  
...  
Keyword(s):  
Coupled Oscillators ◽  
Nonlinear Oscillator ◽  
Mandelbrot Set ◽  
Parameter Plane ◽  
Two Dimensional ◽  
Routes To Chaos ◽  
Nonlinear Coupled Oscillators ◽  
Two Parameter

Abstract Two well-known bifurcation routes to chaos of two-dimensional coupled logistic maps are embedded in a two-parameter plane of a canonical nonlinear oscillator which contains a non-analytic analogon to the Mandelbrot set.

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