Phase pattern switching in star-coupled Wien-bridge oscillators driven by pulse train

There have been many investigations of mutual synchronization and multimode oscillation in coupled oscillators1)–4). Endo et al. have reported the multimode oscillations in various types of the coupled oscillators networks1). The synchronization phenomena in resistively coupled oscillators have been reported2)–4). In particular, we have reported synchronization phenomena observed from N oscillators with the same natural frequency mutually coupled by one resistor3, 4). In these systems, various synchronization phenomena can be observed. Especially, in LC oscillators systems, we have confirmed experimentally that N -phase oscillation can be stably excited when each oscillator has strong nonlinearity3). In this case, there exist (N − 1)! stable phase states according to the initial states. Moreover, we have investigated the coupled system with RC Wien-bridge oscillators. This system is suitable for VLSI implementation because the system does not include any inductors. They also exhibits the “phase-shift synchronization” and we can get 3N−1 different stable phase patterns4). Because these “star-coupled” oscillators exhibit a large number of different steady states, they will be used as a structural element of large scale memories and neural networks. On the other hand, recently, many researches on the networks of the nonlinear elements have been reported 5, 6), because they are important not only as a model for nonlinear systems but also from the viewpoint of biological information processing and their possible engineering applications. Chua et al. have proposed the network of the sparsely interconnected nonlinear elements called cellular neural network (CNN)5). Kaneko has suggested the possibility of the information processing using the network of the nonlinear elements by investigating the globally coupled chaotic elements from various aspects6). Thus much attention has been paid to the approach for such applications from the coupled oscillator systems recently. And also we have proposed the coupled oscillators systems based on star-coupled LC7) or RC8) oscillators systems. These systems also exhibit many different phase patterns and their coupling structures are similar to the CNN’s ones. Therefore, it is considered that they can be used as some kinds of CNN. When we use the coupled oscillators systems as neural networks and large scale memories, it should be an important problem how to control the systems to get the appropriate phase patterns. To achieve the phase pattern control, we have proposed the star-coupled system of Wien-bridge oscillators driven by the periodic pulse train and confirmed that the stimulation of the pulse train can cause the phase pattern switching9). In this system, however, only the phase of the oscillator where the pulse train is directly added switches, but the other oscillators’ phases were not switched. Thus, in this study, we propose two types of star-coupled Wienbridge oscillators whose driving method with pulse train is different. One is the system the number of the driving units are different, the other is the system whose driving unit is at the different place from the previous one. These systems should be helpful for building the phase control units for the coupled oscillators systems.