Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Input-Output Mechanism of the Discrete Chaos Extension
Date
2016-01-01
Author
Akhmet, Marat
Metadata
Show full item record
Item Usage Stats
122
views
0
downloads
Cite This
In this paper, the authors analyze the extension of chaotic dynamics to a particular transformation of a discrete dynamical system. The main result consists in showing that starting from a chaotic map (input), the state variable obtained by adding a linear map and a continuous function of the chaotic state (output) is chaotic as well. These results are based on Devaney's definition of chaos and, for this purpose, this definition is extended to collections of sequences. Several examples are presented to show chaotic dynamics for output systems and an extension of period doubling cascades in coupled systems. The paper then analyzes the existence of homoclinic and heteroclinic orbits for the input and output systems as well as chaos control techniques for the output system in terms of the input system. The last part of the study explores in detail an application to the dynamics of a bacterial infection (gonorrhea) in two distinct heterosexual populations by means of a bidimensional map. Chaotic motion of the system is thus proven by employing the main results of the paper.
URI
https://hdl.handle.net/11511/79373
Collections
Department of Mathematics, Book / Book chapter
Suggestions
OpenMETU
Core
Output-feedback control of linear time-varying and nonlinear systems using the forward propagating Riccati equation
Prach, Anna; Tekinalp, Ozan; Bernstein, Dennis S. (2018-04-01)
For output-feedback control of linear time-varying (LTV) and nonlinear systems, this paper focuses on control based on the forward propagating Riccati equation (FPRE). FPRE control uses dual difference (or differential) Riccati equations that are solved forward in time. Unlike the standard regulator Riccati equation, which propagates backward in time, forward propagation facilitates output-feedback control of both LTV and nonlinear systems expressed in terms of a state-dependent coefficient (SDC). To invest...
Analysis of metal forming by using isogeometric elements
Özdoğan, Yasin; Darendeliler, Haluk; Department of Mechanical Engineering (2018)
In this thesis, a new numerical analysis method named as isogeometric analysis (IGA), based on usage of non-uniform rational basis spline (NURBS) basis functions is studied in order to examine the behavior of parts in the forming processes. NURBS is a mathematical modeling method used for representing any kind of curves, surfaces and 3-D shapes and it is widely used in computer aided design (CAD) software packages since its favorable and flexible nature makes modelling of complex geometries possible. Isogeo...
Outputs bounds for linear systems with repeated input signals: existence, computation and application to vehicle platooning
Saglam, Harun Bugra; Schmidt, Klaus Verner (2018-01-01)
This paper investigates the effect of repeated time-limited input signals on the output excursion of stable, linear time-invariant systems. It is first shown that the maximum norm of the output signal remains bounded if the repeated input signals are separated by a nonzero dwell time. Then a novel method for computing a tight bound on the output signal norm is proposed. The setting of the paper is motivated by a vehicle platooning application, where vehicles repeatedly open/close gaps in order to perform la...
The complexity of topological conjugacy of pointed Cantor minimal systems
Kaya, Burak (2017-05-01)
In this paper, we analyze the complexity of topological conjugacy of pointed Cantor minimal systems from the point of view of descriptive set theory. We prove that the topological conjugacy relation on pointed Cantor minimal systems is Borel bireducible with the Borel equivalence relation Delta(+)(R) on R-N defined by x Delta(+)(R)y double left right arrow {x(i):i is an element of N} = {y(i):i is an element of N}. Moreover, we show that Delta(+)(R) is a lower bound for the Borel complexity of topological co...
Implementation of k-epsilon turbulence models in a two dimensional parallel navier-stokes solver on hybrid grids
Kalkan, Onur Ozan; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2014)
In this thesis, the popular k-ε turbulence model is implemented on a parallel, 2-dimensional, explicit, density-based, finite volume based Navier-Stokes solver works on hybrid grids, HYP2D. Among the other versions available in the open literature, standard version of the k-ε turbulence mode is studied. Launder-Spalding and Chieng-Launder wall functions are adapted to the turbulence model in order to investigate the effects of the strong gradients in the vicinity of the wall on the turbulence. In order to i...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Akhmet,
Input-Output Mechanism of the Discrete Chaos Extension
. 2016, p. 233.