Chaotic operation by a single transistor circuit in the reverse active region

Abstract

In this paper, we present an externally triggered experimental chaotic circuit with a bipolar junction transistor operating in its reverse active region in order to investigate for possible control features in its output phase portraits. Nonlinear time series modeling techniques are applied to analyze the circuit's output voltage oscillations and reveal the presence of chaos, while the chaos itself is achieved by controlling the amplitude of the applied input signal. The phase space, which describes the behavior evolution of a nonlinear system, is reconstructed using the delay embedding theorem suggested by Takens. The time delay used for this reconstruction is chosen after examining the first minimum of the collected data average mutual information, while the sufficient embedding dimension is estimated using the false nearest-neighbor algorithm which has a value of 5. Also the largest Lyapunov exponent is estimated and found equal to 0.020 48. Finally, the phase space embedding based weight predictor algorithm is employed to make a short-term prediction of the chaotic time series for which the system's governing equations may be unknown.

Optoelectronic Chaotic Circuits

“…In this case =77 time steps for chaotic signal across emitter resistor R 2 and =38 steps for chaotic signal across LED resistor R 1 as shown in figure 13. Next, we use the method of False Nearest Neighbors (FNN), [Hanias et al, 2010], in order to estimate the minimum embedding dimension. This method is based on the fact that when the embedding dimension is too small, the trajectory in the phase space will cross itself.…”

Use of recurrence plot and recurrence quantification analysis in Taiwan unemployment rate time series

“…Since there is no solid rule of how to choose W , we may choose to take the time at which the autocorrelation function ACF has dropped to 1/e (0.3678) of its initial value [28]. As shown in Fig.…”

“…We choose 10 as the threshold value and 57 as the Theiler window to detect FNN. The dimension m can obtained when FNN percentage falls below some limit, typically set to 1% [28]. Fig.…”

Short-term prediction of dynamical behavior of flame front instability induced by radiative heat loss

“…In the field of nonlinear physics, nonlinear forecasting based on orbital instability in the phase space or neural network theory has been shown to ensure good performance in the short-term prediction of deterministic chaos. 15,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] This can be considered to be an inverse approach in the sense that the underlying dynamics is expressed by a predictive model constructed from the observed temporal behavior. The importance of the inverse approach has previously been discussed by some of the authors.…”