Aybar, I.K.

Conference Object | 2012 | CHAOS 2012 - 5th Chaotic Modeling and Simulation International Conference, Proceedings , pp.271 - 276

A relation between the optimal solution of the optimization problem and the stability and bifurcation properties of the corresponding dynamical system is suggested in this work. There exists a relation between the optimal solution of an optimization problem and an equilibrium point of a dynamical system. In this sense stability properties, Lyapunov exponents and bifurcations of the resulting dynamical systems can be studied. © 2012 5th Chaotic Modeling and Simulation International Conference All Rights Reserved

Aybar, O.O. | Hacinliyan, A.S. | Ayba, I.K. | Koseyan, K. | Deruni, B.

Conference Object | 2012 | CHAOS 2012 - 5th Chaotic Modeling and Simulation International Conference, Proceedings , pp.43 - 49

A motivation for looking at chaos in the classical realizations of the Yang-Mills or Yang Mills augmented by Higgs equations is the importance of this system in the initial (in)stability at big bang, since in the initial stages all interactions were of the same strength and were based on non abelian gauge theories, of which the SU(2) Yang Mills is a first example. In this study we consider the following two particle effective Hamiltonian suggested by Biro, Matinyan and Müller: H=px2+py2-b2y2/2/2 -x2y2+1+1/2a2x2+b2y2). © 2012 5th Chaotic Modeling and Simulation International Conference All Rights Reserved

Akkaya, E.E. | Yildirim, A.H. | Hacinliyan, A.S.

Conference Object | 2019 | CHAOS 2014 - Proceedings: 7th Chaotic Modeling and Simulation International Conference , pp.27 - 32

Bitcoin was introduced in 2009 as an open source, peer-to-peer payment network for sending payments using a client software. Bitcoin has lower transaction fees compared to credit card processors which makes it a preferable transaction agency for merchants. In this paper, daily exchange prices of bitcoin in the years of 2011 to 2014 for different currencies have been analyzed using nonlinear time series analysis techniques. To apply the analysis, phase space is reconstructed by using delay time obtained from mutual information and autocorrelation of data with an embedding dimension suggested by the false nearest neighbors method. Cal . . .culated positive Lyapunov exponents indicate a possible chaotic behavior. © 2014 ISAS Daha fazlası Daha az

Alan, N. | Aybar, I.K. | Aybar, O.O. | Hacinliyan, A.S.

Conference Object | 2012 | CHAOS 2012 - 5th Chaotic Modeling and Simulation International Conference, Proceedings , pp.19 - 25

In this study, the International market gold prices over the last 31 years were analyzed for trends by five different methods, linear trend analysis, ARMA analysis, Rescaled range analysis, attractor reconstruction and maximal Lyapunov Exponent, detrended fluctuation analysis. Unfortunately not all methods give consistent results. The linear analysis reveals three regions with different trends. This is not supported by the rescaled range or detrended fluctuation analysis results. The maximal Lyapunov exponent calculation reveals chaotic behavior. The detrended fluctuation analysis reveals behavior close to brown noise. This is not c . . .orroborated by the rescaled range analysis, which indicates anti persistent behavior. The ARMA model implies first differencing that indicates a strong underlying linear trend. Combining these results, one probable explanation is that the strong linear trend, (also corroborated by ARMA analysis) affects the rescaled range calculation, because of its dependence on extreme values. The detrended fluctuation analysis removes this trend and reveals brown noise. This is consistent with a maximal positive Lyapunov exponent. Hence, we have a linear trend plus brown noise and neither of these two effects is dominant. © 2012 5th Chaotic Modeling and Simulation International Conference All Rights Reserve Daha fazlası Daha az