Analytical expressions for power spectral density issued from one-dimensional continuous piecewise linear maps with three slopes

2014 ◽  
Vol 94 ◽  
pp. 149-157 ◽  
Author(s):  
Kais Feltekh ◽  
Danièle Fournier-Prunaret ◽  
Safya Belghith
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Piecewise Linear ◽  
One Dimensional ◽  
Power Spectral ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Analytical Expressions

scholarly journals Iteration of piecewise linear maps on an interval

1981 ◽  
Vol 24 (3) ◽  
pp. 433-451 ◽  
Author(s):  
James B. McGuire ◽  
Colin J. Thompson
Keyword(s):  
Invariant Measures ◽  
Piecewise Linear ◽  
Point Of View ◽  
Complete Analysis ◽  
Functional Composition ◽  
One Dimensional ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Parameter Values ◽  
Dense Set

A complete analysis is given of the iterative properties of two piece-piecewise linear maps on an interval, from the point of view of a doubling transformation obtained by functional composition and rescaling. We show how invariant measures may be constructed for such maps and that parameter values where this may be done form a dense set in a one-dimensional subset of parameter space.

Nonlinear Dynamics of Trajectories Generated by Fully-Stretching Piecewise Linear Maps

2014 ◽  
Vol 24 (05) ◽  
pp. 1450071 ◽  
Author(s):  
T. Papamarkou ◽  
A. J. Lawrance
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Exponent ◽  
Piecewise Linear ◽  
Nonlinear Dynamical ◽  
Chaotic Orbits ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
The Mean ◽  
Dynamical Properties ◽  
Analytical Expressions

This paper focuses on the nonlinear dynamical properties of chaotic orbits iteratively generated by maps composed of linear branches which expand across the whole map range. The nonlinear dynamics of such orbits involve both their statistical and chaotic properties. More specifically, analytical expressions are provided for the mean-adjusted quadratic autocorrelation function (ACF) and for the Lyapunov exponent of trajectories produced by the considered collection of piecewise linear maps.

PERIOD ADDING IN PIECEWISE LINEAR MAPS WITH TWO DISCONTINUITIES

2012 ◽  
Vol 22 (03) ◽  
pp. 1250068 ◽  
Author(s):  
FABIO TRAMONTANA ◽  
LAURA GARDINI ◽  
VIKTOR AVRUTIN ◽  
MICHAEL SCHANZ
Keyword(s):  
Piecewise Linear ◽  
Discontinuity Point ◽  
Big Bang ◽  
One Dimensional ◽  
Piecewise Linear Map ◽  
Stable Regime ◽  
Bifurcation Points ◽  
Border Collision Bifurcations ◽  
Linear Maps ◽  
Piecewise Linear Maps

In this work we consider the border collision bifurcations occurring in a one-dimensional piecewise linear map with two discontinuity points. The map, motivated by an economic application, is written in a generic form and considered in the stable regime, with all slopes between zero and one. We prove that the period adding structures occur in maps with more than one discontinuity points and that the Leonov's method to calculate the bifurcation curves forming these structures is applicable also in this case. We demonstrate the existence of particular codimension-2 bifurcation (big-bang bifurcation) points in the parameter space, from which infinitely many bifurcation curves are issuing associated with cycles involving several partitions. We describe how the bifurcation structure of a map with one discontinuity is modified by the introduction of a second discontinuity point, which causes orbits to appear located on three partitions and organized again in a period-adding structure. We also describe particular codimension-2 bifurcation points which represent limit sets of doubly infinite sequences of bifurcation curves and appear due to the existence of two discontinuities.

DESIGN OF ONE-DIMENSIONAL CHAOTIC MAPS WITH PRESCRIBED STATISTICAL PROPERTIES

1995 ◽  
Vol 05 (06) ◽  
pp. 1585-1598 ◽  
Author(s):  
A. BARANOVSKY ◽  
D. DAEMS
Keyword(s):  
Inverse Problem ◽  
Correlation Function ◽  
Invariant Measure ◽  
Wide Class ◽  
Chaotic Maps ◽  
Piecewise Linear ◽  
Statistical Properties ◽  
One Dimensional ◽  
Linear Maps ◽  
Piecewise Linear Maps

The statistical properties of a wide class of 1D piecewise linear Markov maps are compiled. The method used enables one to address analytically the inverse problem of designing a map with a prescribed correlation function. This class of piecewise linear maps is then used as a system of reference to analyze non-Markov piecewise linear maps and to design maps with given invariant measure and correlation function.

Analytical Expressions for the Power Spectral Density of CP-OFDM and ZP-OFDM Signals

2010 ◽  
Vol 17 (4) ◽  
pp. 371-374 ◽  
Author(s):  
T. van Waterschoot ◽  
V. Le Nir ◽  
J. Duplicy ◽  
M. Moonen
Keyword(s):  
Spectral Density ◽  
Power Spectral Density ◽  
Power Spectral ◽  
Analytical Expressions ◽  
Ofdm Signals
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