A PICTURE BOOK OF TWO FAMILIES OF CUBIC MAPS

1993 ◽  
Vol 04 (03) ◽  
pp. 553-568 ◽  
Author(s):  
FERNANDO CABRAL ◽  
ALEXANDRE LAGO ◽  
JASON A. C. GALLAS
Keyword(s):  
Dynamical Systems ◽  
High Resolution ◽  
Parameter Space ◽  
Picture Book ◽  
Initial Conditions ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Two Parameters ◽  
The Way

This paper reports high-resolution isoperiodic diagrams for two model-families of dynamical systems characterised by one-dimensional maps depending on two parameters. We present a comparison of both diagrams, investigating the way in which initial conditions affect isoperiodic sets in the parameter space of both systems and the similarities between them. Although both models represent quite different dynamical systems, they are found to have many properties in common in their space of parameters.

Application of a Generalized Frobenius-Perron Operator Scheme to Multivariate Nonlinear Dynamical Systems

1995 ◽  
Vol 50 (12) ◽  
pp. 1123-1127
Author(s):  
R. Stoop ◽  
W.-H. Steeb
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Free Energies ◽  
Nonlinear Dynamical ◽  
One Dimensional ◽  
One Dimensional Maps ◽  
Operator Scheme

Abstract The concept of generalized Frobenius-Perron operators is applied to multivariante nonlinear dynamical systems, and the associated generalized free energies are investigated. As important applications, diffusion-related free energies obtained from normally and superlinearly diffusive one-dimensional maps are discussed.

On the dynamics of the Tent function - Phase diagrams

2016 ◽  
Vol 7 (4) ◽  
pp. 261
Author(s):  
Prince Amponsah Kwabi ◽  
William Obeng Denteh ◽  
Richard Kena Boadi
Keyword(s):  
Dynamical Systems ◽  
Phase Diagrams ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Topological Dynamical System ◽  
Topological Transitivity ◽  
Tent Map ◽  
One Dimensional ◽  
Definition Of ◽  
Topological Dynamical Systems

This paper focuses on the study of a one-dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.

scholarly journals Development of High-Resolution Total Variation Diminishing Scheme for Linear Hyperbolic Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Rabie A. Abu Saleem ◽  
Tomasz Kozlowski
Keyword(s):  
High Resolution ◽  
Total Variation ◽  
Initial Conditions ◽  
Hyperbolic Problems ◽  
Total Variation Diminishing ◽  
One Dimensional ◽  
Flux Limiter ◽  
Variation Diminishing ◽  
Flux Limiters ◽  
Theta Method

A high-resolution, total variation diminishing (TVD) stable scheme is derived for scalar hyperbolic problems using the method of flux limiters. The scheme was constructed by combining the 1st-order upwind scheme and the 3rd-order quadratic upstream interpolation scheme (QUICK) using new flux limiter function. The new flux limiter function was established by imposing several conditions to ensure the TVD properties of the scheme. For temporal discretization, the theta method was used, and values for the parameter θ were chosen such that the scheme is unconditionally stable. Numerical results are presented for one-dimensional pure advection problems with smooth and discontinuous initial conditions and are compared to those of other known numerical schemes. The results show that the proposed numerical method is stable and of higher order than other common schemes.

BORDER COLLISION BIFURCATIONS IN 1D PWL MAP WITH ONE DISCONTINUITY AND NEGATIVE JUMP: USE OF THE FIRST RETURN MAP

2010 ◽  
Vol 20 (11) ◽  
pp. 3529-3547 ◽  
Author(s):  
LAURA GARDINI ◽  
FABIO TRAMONTANA
Keyword(s):  
Parameter Space ◽  
Complete Characterization ◽  
One Dimensional ◽  
Return Map ◽  
Border Collision Bifurcations ◽  
One Dimensional Maps ◽  
Negative Jump

The aim of this work is to study discontinuous one-dimensional maps in the case of slopes and offsets having opposite signs. Such models represent the dynamics of applied systems in several disciplines. We analyze in particular attracting cycles, their border collision bifurcations and the properties of the periodicity regions in the parameter space. The peculiarity of this family is that we can make use of the technical instrument of the first return map. With this, we can rigorously prove properties which were known numerically, as well as prove new ones, giving a complete characterization of the overlapping periodicity regions.

scholarly journals Dweiltime Analysis of Symmetry-Breaking Dynamical Systems

1995 ◽  
Vol 50 (12) ◽  
pp. 1117-1122 ◽  
Author(s):  
J. Vollmer ◽  
J. Peinke ◽  
A. Okniński
Keyword(s):  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Dwell Time ◽  
Initial Conditions ◽  
Dissipative Systems ◽  
Time Analysis ◽  
Chaotic Scattering ◽  
One Dimensional ◽  
Basin Boundary ◽  
Sensitive Dependence

Abstract Dweiltime analysis is known to characterize saddles giving rise to chaotic scattering. In the present paper it is used to characterize the dependence on initial conditions of the attractor approached by a trajectory in dissipative systems described by one-dimensional, noninvertible mappings which show symmetry breaking. There may be symmetry-related attractors in these systems, and which attractor is approached may depend sensitively on the initial conditions. Dwell-time analysis is useful in this context because it allows to visualize in another way the repellers on the basin boundary which cause this sensitive dependence.

STEM characterization of a 6Å diameter Mo3Se3 fiber

1993 ◽  
Vol 51 ◽  
pp. 820-821
Author(s):  
M. Hornbostel ◽  
F.J. DiSalvo ◽  
S. Hillyard ◽  
J. Silcox
Keyword(s):  
High Resolution ◽  
Propylene Carbonate ◽  
Vacuum Evaporation ◽  
Free Standing ◽  
Polar Solvents ◽  
One Dimensional ◽  
Carbon Substrates ◽  
High Resolution Microscopy ◽  
The Way

LiMo3Se3 is a highly anisotropic conductor containing 6Å diameter one dimensional chains of Mo3Se3 triangles. This compound can be dissolved in polar solvents to produce solutions containing micron length Mo3Se3 fibers. Choice of solvent and solution concentrations allows some control of fiber diameters, from a few hundred angstroms down to the molecular limit of a single 6Å diameter chain. These fibers have been deposited from solution on holey carbon substrates by vacuum evaporation of the solvent to produce free-standing, one dimensional wires.High resolution microscopy at 100kV was carried out in a VG HB501A STEM and confirms the presence of many different sized bundles extending all the way down to the single strands. Figure 1a shows an ADF image of a medium sized strand which commonly occured in a sample prepared with the solvent propylene carbonate. The flexibility of the fiber and its seeming attraction to the edges of carbon holes is apparent as it snakes its way along the surface.

scholarly journals The role of extreme orbits in the global organization of periodic regions in parameter space for one dimensional maps

2016 ◽  
Vol 380 (18-19) ◽  
pp. 1610-1614 ◽  
Author(s):  
Diogo Ricardo da Costa ◽  
Matheus Hansen ◽  
Gustavo Guarise ◽  
Rene O. Medrano-T ◽  
Edson D. Leonel
Keyword(s):  
Parameter Space ◽  
One Dimensional ◽  
Global Organization ◽  
One Dimensional Maps
Sign in / Sign up

Export Citation Format

Share Document