Relaxation and chaotic behavior in time varying phenomena

The time evolutions of transient current data for As2Te3(In) thin films were measured at different electric fields for the dc voltages of 0.001 V, 0.002 V, 0.005 V, 0.01 V, 0.1 V, 0.5 V and 1 V at room temperature (296 K – 23 °C) and also for the dc voltages of 0.001 V, 0.002 V, 0.005 V, 0.01 V and 0.1 V at temperatures of 313 K (40 °C), 333 K (60 °C) and 353 K (80 °C). Transient current was analyzed by means of time series analysis in order to identify different conduction regimes. The maximal Lyapunov exponents for the transient currents were calculated. Positive maximal Lyapunov exponents reflected electric field and temperature dependencies with positive Lyapunov exponents. Existence of a positive Lyapunov exponent means sensitive dependence on initial conditions and As2Te3(In) is known to have memory effects hence different initial conditions for each dc current measurement. Detrended Fluctuation Analysis was utilized to characterize the behavior of dc current time series which is invariant to initial conditions. Detrended Fluctuation Analysis identified three different conduction regimes with multiple conduction mechanisms in terms of applied electric fields. Moreover, crossovers based on current behaviors of As2Te3(In) thin films at two different conduction regimes were observed for different temperatures by Detrended Fluctuation Analysis method. Possible conduction mechanisms were decided and extensively discussed with respect to results of scaling exponents which depend on crossover phenomena. On the other hand, it was determined that both the artificial data as current versus time which was simulated by Mackey-Glass equation and the empirical data which includes current values varying with time had similar maximal Lyapunov exponents. Hence, delay differential equations such as the Mackey-Glass equation can be used as suitable simulation methods to analyze and predict transient current mechanism of As2Te3(In) glass substrates at micro-scale concept. As final step, Stretched exponential parametrization was used for fitting the modified function of stretched exponential behavior to first 4000 data points of our empirical data sets under 0.1 V at macro-scale concept. Thereupon, it was observed that both relaxation times and stretched exponent values increase with temperature.