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Yayın Signals of chaotic behavior in PMMA(Pergamon-Elsevier Science, 2003-07) Hacınlıyan, Avadis Simon; Skarlatos, Yani; Şahin, Gökhan; Akın, Güzin GülsünThe time evolution of the current passing through PMMA polymer thin films under 10 V at 23degreesC (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.Yayın Normal forms and nonlocal chaotic behavior in Sprott systems(Pergamon-Elsevier Science, 2003-06) Perdahçı, Nazım Ziya; Hacınlıyan, Avadis SimonThe Sprott systems are used as benchmarks for investigating the applicability of the normal form transformation in estimating nonlocal properties of attractors such as positive and zero Liapunov exponents. Possibility of a relation between complex conjugate eigenvalue pairs and zero Liapunov exponents; conditions under which the normal form expansion can represent the attractor; an averaging relation for the largest Liapunov exponent based on this representation are studied. Nonlinear transformations that can change the order of a resonance are considered. In spite of their convergence problems, it is seen that the normal form approach can give reasonable estimates of nonlocal properties of attractors near Hopf bifurcations.Yayın A higher-order model for transverse waves in a generalized elastic solid(Pergamon-Elsevier Science, 2002-11) Hacınlıyan, Avadis Simon; Erbay, SaadetIn the present study, the nonlinear modulation of transverse waves propagating in a generalized elastic solid is studied using a multi-scale expansion of quasi-monochromatic wave solutions. In particular, to include the higher-order nonlinear and dispersive effects in the evolution equations, higher-order perturbation equations are considered, and it is shown that the modulation of two transverse waves is governed by a pair of the coupled higher-order nonlinear Schrodinger (HONLS) equations. In the absence of one of the transverse waves, the coupled HONLS equations reduce to the single HONLS equation that has already been obtained in the context of nonlinear optics. Some special solutions to the coupled HONLS equations are also presented.
