International Teacher Education Conference 2014 1

International Teacher Education Conference 2014
Computer Education Example: Chaotic Secure Communication Simulations
Yılmaz UYAROĞLU, Mustafa KARAKAYIŞ, M.Ali YALÇIN
SAKARYA UNIVERSITY, SAKARYA, TURKİYE, E-posta: uyaroglu@sakarya.edu.tr, yalcin@sakarya.edu.tr
Abstract
In this work nonlinear dynamics, synchronization and secure communication by synchronization of Rucklidge
Attractor is investigated and matlab simulation results are given for engineer students.
Keywords: Rucklidge Attractor, chaos, synchronization, chaotic masking.
1. Introduction
The human has continuously researched the ways of transmitting information beyond normal borders for
thousands of years. With enhancement of technology, researches have focused on secure and private information
transmission. Secure and private transmission of information with chaos/chaotic signals has become an
interesting subject due to dynamical, tender dependency to introduction, nonlinear structure of chaos/chaotic
signals. In order to demodulate the transmitted information -modulated with chaotic signals- at receiver, chaotic
synchronization concept has occurred. With observation of synchronization at subsystems of chaotic systems,
communication system design, using chaotic signals as carrier, has become one of the significant research areas
of recent years.
Chaotic Rucklidge dynamical system model was built up at 1991 to derive models for two-dimensional
convection in a horizontal layer of Bossiness fluid with lateral constraints with hypothesis that “In certain
parameter regimes, it is possible to derive third-order sets of ordinary differential equations that are
asymptotically exact descriptions of weakly nonlinear double convection and that exhibit chaotic behavior.” [1]
This paper is organized as follows. In section 2, the nonlinear equations of Rucklidge and its dynamical behavior
are introduced with matlab simulations. In section 3, synchronization of Rucklidge attractors with pecorra-carroll
method was simulated. In section 4, secure communication by using Rucklidge attractor with chaotic masking
was simulated. Finally we summarize our work in the Conclusion [2].
2. Rucklidge attractor and It’s chaotic behavior
Rucklidge stystems equations are;
.
X = −KX
+ LY − YZ
.
Y = X
.
2
Z = −Z
+ Y
(1)
Where K and L are system constants.
If equation (1) is solved by using Runge-Kuntta method on Matlab with initial values
X(0) = 1, Y(0) = 0, Z(0) = 4.
5 and for system constants K = 2 , L = 6. 7 as could be seen over Figure-1 and Figure-2
Rucklidge system equations shows chaotic behavior for the given conditions.
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