# Synchronization of Analog-Discrete Chaotic Systems for Wireless Sensor Network Design
The first one is the Pecora-Carroll procedure [19], where synchronization is achieved by substituting the state variable of one chaotic system with the state variable of the other chaotic system. The second technique is error feedback control [20], where the difference of asynchronous chaos signals is used to adjust the state of one chaotic system. Several works [21; 22; 23; 24] have explored the approaches for chaos oscillators' synchronization. The Pecora-Carroll technique is simpler in implementation but requires one state variable of the chaotic system to act as a synchronization signal. The error feedback is more elaborate in implementation, but the synchronization signal is not limited to only ensuring synchronization. The attention towards synchronizing an analog chaos oscillator to its discrete counterpart and vice versa has received more attention in recent years. Two studies [25; 26] explored only the discrete-analog synchronization of Rossler chaos oscillator. The current work studies the performance of analog-discrete and discrete-analog chaotic synchronization using the Pecora-Carroll technique for the Vilnius and RC chaos oscillators. The first study explores the quality of analog-discrete and discrete-analog synchronization in noisy conditions. As synchronization is applied in wireless data transmission, the question of synchronization's noise immunity is relevant and is commonly explored for chaos-based communications [27; 28]. The second study explores the speed of analog-discrete and discrete-analog synchronization and desynchronization. This study is necessary to understand the time required for synchronization to occur and the time for the chaos oscillator to diverge. This work has multiple novelty points. First, the Vilnius [29] and RC [30] chaos oscillators were not widely explored regarding analog-discrete model development and synchronization. The second is that the two studies have simulation-based and experimental approaches. The simulation approach uses LTSpice to model the behavior of the analog chaos oscillator, while the experimental approach uses the hardware prototype of the oscillator implemented in PCB. This allows for comparing the behavior of the LTSpice and hardware models. The third novelty point is the synchronization and desynchronization speed study. To the best of the author's knowledge, the given direction was generally overlooked, especially in the discrete-analog and analog-discrete cases, with one prime work being [31]. The results of this work open wide possibilities for the further development of chaos-based communication systems, making the proposed chaos-based WSN system possible, considering the previously developed chaos-based communication systems by the research group [32; 33; 34]. The paper is organized as follows: Section 2 describes the chaos oscillators used in this work, their discrete and LTSpice models, as well as the hardware prototype. Section 3 presents the study on the performance of Pecora-Carroll analog-discrete and discrete-analog synchronization noise immunity. The section details the implementation of the study and analyzes the acquired results. Section 4 presents the study on the performance of Pecora-Carroll analog-discrete and discrete-analog synchronization and desynchronization time, elaborating on the experiment setup and analyzing the acquired results. The final section discusses the results of the two studies and their future impact on the development of chaos-based communication systems and concludes the work.