A. Hacinliyan

Signals of chaotic behavior in PMMA

Abstract The time evolution of the current passing through PMMA polymer thin films under 10 V at 23 °C (296 K) was sampled at intervals ranging from 1 to 20 s. The data showed chaotic behavior in the context of pinned charge density waves [Phys. Rev. B 41 (1990) 11522]. The resultant time series has been analyzed by means of TISEAN, time series analysis software [The TISEAN package CHAOS 9 (1999) 413]. The analysis has revealed a positive maximal Lyapunov exponent. This is also corroborated by a calculation of the fractal dimension and application of the Kaplan–Yorke conjecture. In the analysis two widely separated time scales have been observed; the first zero crossing of the correlation function at 8380 s and the first marked minimum of the average mutual information at 40 s.

Possible stretched exponential parametrization for humidity absorption in polymers

Polymer thin films have irregular transient current characteristics under constant voltage. In hydrophilic and hydrophobic polymers, the irregularity is also known to depend on the humidity absorbed by the polymer sample. Different stretched exponential models are studied and it is shown that the absorption of humidity as a function of time can be adequately modelled by a class of these stretched exponential absorption models.

CHARACTERIZATION OF CHAOTICITY IN THE TRANSIENT CURRENT THROUGH PMMA THIN FILMS

Chaotic behavior in the transient current through thin Aluminum-PMMA-Aluminum films has been analyzed for times ranging up to 30,000s, in the temperature range 293–363K for applied voltages in the range 10–80V. Time series analysis reveals a positive Lyapunov exponent consistently and reproducibly throughout this range. Power law relaxation as reflected by the autocorrelation function and the positive Lyapunov exponent show parallel behaviors as a function of applied electric field.

Chaoticity analysis of the current through pure, hydrogenated and hydrophobically modified PEG-Si thin films under varying relative humidity

Polyethylene Glycol has an irregular current characteristic under constant voltage and slowly varying relative humidity. The current through a thin film of Gamma-isocyanatopropyltriethoxysilane added Polyethylene glycol (PEG-Si), its hydrogenated and hydrophobically modified forms, as a function of increasing relative humidity at equal time steps is analyzed for chaoticity. We suggest that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended uctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. DFA also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. We also suggest that the irregular behavior of the current through PEG-Si can be reduced by hydrogenating and hydrophobically modifying PEG-Si and the improvement in stability can be confirmed by our study.

Transforming to Chaos by Normal Forms

Roepstorff’s algebraic approach for the Lyapunov exponent calculation implies an approximation scheme. The possibility of using normal forms as this approx-imation for estimating Lyapunov exponents and attractor extents in resonant sys-tems with the Hopf bifurcation property is studied. The Khomeriki NMR system has been studied as an example of the inconsistency between different chaoticity criteria.

Signs and approximate magnitudes of Lyapunov exponents in continuous time dynamical systems

Methods for algebraically determining the signs and the magnitudes of Lyapunov exponents of a given dynamical system are studied. The existence of zero Lyapunov exponents for the Toda, Henon–Heiles, and Rossler systems are shown. The approximate Lyapunov spectra of Lorenz and Rossler systems are computed.

Stability of gravitational merons

Abstract We find that in gravitational models containing Yang-Mills fields merons are unstable.

Bifurcations in Van der Pol-Like Systems

Generalizations of the Van der Pol system with polynomial interactions involving additional parameters are studied in order to understand qualitative properties such as stability and additional bifurcations in these generalized Van der Pol systems. The generalizations include the one known as the Duffing-Van der Pol system which has properties similar to those of the Maxwell-Bloch system.

Chaoticity in the time evolution of foreign currency exchange rates in Turkey

Tools from chaos theory that have found recent use in analysing financial markets have been applied to the US Dollar and Euro buying and selling rates against the Turkish currency. The reason for choosing the foreign exchange rate in this analysis is the fact that foreign currency is an indicator of not only the globalization of economy but also savings and investment. In order to test the globality assumption and to ascertain the degree of involvement of local conditions in Turkey, the Euro and US dollar exchange rates have been subjected to the same analysis.

Simulating a dynamical system in the presence of a 1/f noise

Abstract Chaotic systems that possess strange attractors or exhibit type I or III intermittencies are known to yield a 1/ f noise in their power spectra. In this work, simulation of such systems is considered, and bounds for the sampling frequencies on them are sought. Also, several limits on the duration of simulation are discussed. Developed ideas are demonstrated over work bench chaotic systems.