First Experimental Observation of Generalized Synchronization Phenomena in Microwave Oscillators

Abstract

In this Letter we report for the first time on the experimental observation of the generalized synchronization regime in the microwave electronic systems, namely, in the multicavity klystron generators. A new approach devoted to the generalized synchronization detection has been developed. The experimental observations are in the excellent agreement with the results of numerical simulation. The observed phenomena gives a strong potential for new applications requiring microwave chaotic signals. Chaotic synchronization is one of the fundamental phenomena, widely studied recently, having both theoretical and applied significance [1]. One of the interesting and intricate types of the synchronous behavior of unidirectionally coupled chaotic oscillators is the generalized synchronization (GS) [2,3], which means the presence a functional relation between the dynamics of the drive and response chaotic systems, though this relation may be very complicated and its explicit form cannot be found in most cases. Remarkably, that practically all studies of the generalized synchronization phenomenon deal with the low-dimensional model systems or the low frequency oscillators. Even if generalized synchronization in lasers is studied, the oscillations of the total intensity of the laser output are usually considered whose frequency is in the megahertz range, with the oscillator dynamics being described by the system of the ordinary differential equations [4]. The more complicated objects with the infinite dimensional phase space (such as spatially extended systems (see, e.g., [5]) or oscillators with the delayed feedback) are considered from the point of view of generalized synchronization rarely, and, practically always, numerically.In this Letter we report for the first time on the experimental revelation of generalized synchronization in the microwave systems with the infinite dimensional phase space, namely, in the multicavity klystron oscillators with the delayed feedback. Along with the theoretical interest this study is also important from the point of view of the practical purposes of communication, where the microwave range signals are used very widely.To detect the onset of generalized synchronization in the experiment a new approach being applicable to the microwave systems has been developed. Actually, there are various techniques for detecting the presence of GS between chaotic oscillators, such as the method of nearest neighbors [6] or the auxiliary system approach [2]. It is also possible to calculate the conditional Lyapunov exponents [7] to reveal the generalized synchronization regime. Unfortunately, these approaches are often difficult (or impossible) to implement in the experimental measurements (specifically, in the microwave range), due to the presence of noise and lack of the precisions. Therefore, in this Letter we propose the radically different approach which may deal with the chaotic oscillators of the microwave range to detect experimentally the onset of the generalized synchronization regime. Moreove...

Subterahertz Chaos Generation by Coupling a Superlattice to a Linear Resonator

“…We believe that the phenomena of linear resonators described here are applicable to other NDC solid-state devices, including Gunn diodes [42]. The chaotic high-frequency oscillations observed in our experiments may have technological applications in, for example, nonlinear antennas, broadband radar [43][44][45][46][47][48], and chaos-based logic [49,50]. The latter also plays a crucial role in modern chaos-based communication systems [30,31].…”

Binary generalized synchronization

“…This kind of synchronous behavior means the state vectors of the interacting chaotic systems being in the generalized synchronization regime are related with each other. It has been observed in many systems both numerically [43,[49][50][51] and experimentally [46,52,53].…”

Finite-time synchronization of tunnel-diode-based chaotic oscillators

“…Considering the frequency capability of the tunnel diode, it can be used as an efficient source for chaotic signals in wireless communications; in particular, H.-P. Ren et al [20] show that, for some particular chaotic signals, the Lyapunov exponents remain unaltered through multipath propagation, thus making these systems able to sustain communications with chaotic signals. However, experimental observations of generalized synchronization phenomena in microwave oscillators have been done by B. S. Dmitriev et al [21], and their application to secure communications has been carried out by A. A. Koronovskii et al [22].…”

“…A. Koronovskii et al [22]. Nevertheless, the synchronization schemes used in [20][21][22] are dealing with asymptotical synchronization and can only guarantee that two systems achieve synchronization as time tends to infinity, while in real-world applications one always expects that two systems achieve synchronization within a finite and/or predetermined time. Besides, finite-time synchronization has been confirmed to have better robustness against parametric and external disturbances than the asymptotical one [23,24]-thus, the importance of studying finite-time synchronization of chaotic systems.…”