## 3 Chaos Oscillator Synchronization Noise Immunity
### Result Analyses  
This study analyzes the performance of Colpitts and Vilnius chaos oscillators in different drive-response system configurations within a noisy channel. The goal is to evaluate synchronization performance across different configurations and identify the most robust configuration. Figure 5 presents the study results for the Colpitts chaos oscillator. The \(x\)-axis represents the SNR levels but is flipped to encourage a more convenient interpretation. The \(y\)-axis represents the correlation coefficient, which quantifies the synchronization quality. The figure contains six curves, each pair corresponding to a specific configuration, as summarized in Table 1. Each pair represents the correlation between \(X\) and \(X^{\prime}\) and \(Y\) and \(Y^{\prime}\), illustrating how synchronization is maintained under different noise conditions. Examining Figure 5, it can be observed that \(X^{\prime}\) and \(Y^{\prime}\) signals synchronize differently for each SNR level. When \(v_{RL}\) is used as the synchronization signal, the system fails to achieve synchronization in the drive-response configuration. When \(v_{\text{CI}}\) is employed, \(X^{\prime}\) and \(Y^{\prime}\) (corresponding to \(v_{\text{C2}}\) and \(v_{RL}\)) synchronize at different levels for the same SNR values. A similar trend is observed when \(v_{\text{C2}}\) is used as the synchronization signal; however, \(X^{\prime}\) and \(Y^{\prime}\) synchronize at different levels and show smaller correlation coefficients in this configuration. Figure 6 illustrates the synchronization noise immunity across all three configurations for the Vilnius chaos oscillator. Like Figure 5, it consists of six curves, where each pair  
\begin{table}
\begin{tabular}{c c c|c c c} \hline \hline \multicolumn{2}{c|}{**Colpitts Chaos Oscillator**} & \multicolumn{3}{c}{**Vilnius Chaos Oscillator**} \\ \hline
**X** & **Y** & **Z** & **X** & **Y** & **Z** \\ \hline \(v_{\text{C1}}\) & \(v_{\text{C2}}\) & \(v_{RL}\) & \(v_{\text{C1}}\) & \(v_{\text{C2}}\) & \(v_{R1}\) \\ \(v_{RL}\) & \(v_{\text  
represents the correlation between \(X\) and \(X^{\prime}\) and \(Y\) and \(Y^{\prime}\), corresponding to a specific configuration described in Table 1.  
When \(v_{\text{Cl}}\) is used for synchronization, the response oscillator signals \(v_{\text{C2}}\) and \(v_{\text{R1}}\) do not synchronize at the same level for a given SNR value. In contrast, when \(v_{\text{C2}}\) is the synchronization signal, \(v_{\text{C1}}\) and \(v_{\text{R1}}\) synchronize at the same level, as the two curves overlap entirely. Additionally, this configuration achieves synchronization at lower SNR values than others. When \(v_{\text{R1}}\) is selected as the synchronization signal, an imbalance in synchronization levels is observed, similar to the case of \(v_{\text{C1}}\). Comparing the results for Colpitts and Vilnius oscillators, it is evident that for the Vilnius chaos oscillator, all three configurations achieve synchronization once the noise level is sufficiently low. In contrast, the Colpitts oscillator demonstrates reliable synchronization only in one configuration when \(v_{\text{C1}}\) is used as the synchronization signal. The synchronization with the considerably lower correlation level occurs in the \(v_{\text{C2}}\) configuration. Additionally, one configuration exists for the Colpitts oscillator in which synchronization is never achieved. The results suggest that the Colpitts oscillator exhibits a more restrictive synchronization behavior due to its circuit topology, nonlinear characteristics, and strong variable coupling, which limit the effectiveness of synchronization in some configurations. In contrast, the Vilnius chaos oscillator provides more flexible synchronization possibilities, allowing multiple high-correlation configurations. Another important observation is the presence of synchronization imbalances across different configurations for oscillators at the same SNR level.