In this study, the propagation phenomena of phase differences under 180 degrees between adjacent oscillators can be observed on coupled oscillators by inductors as a lattice. The phenomenon can be observed in transient states. We call the phenomenon "phase-waves." We explain the propagation and the reflection mechanisms of the phase-waves using frequencies of each oscillator and phase differences between adjacent oscillators. Furthermore, we discover to observe an other wave on the above same circuit. The wave can be observed in steady states. We call the wave "phase-inversion wave." We clarify a region which can be observed the phase-inversion waves.

Abstract-In our previous study, we discovered phaseinversion waves on the lattice shape system. The phase-inversion waves are phenomena changing phase states between adjacent oscillators from in-phase to anti-phase or from anti-phase to in-phase and continuously. The phase-inversion waves can be observed in steady states. In this study, we observe and analyze propagation mechanisms of the phase-inversion waves in the lattice shape system. Furthermore, we predict air temperature data by using the lattice shape system. I. INTRODUCTIONIn this world, many kind of synchronization phenomenon can be observed. For example, we can observe the motions of many planets, schools of sardines, the synchronization of fireflies, and so on. The synchronization phenomenon is a field which catches interest of many researchers. Then, the studies of synchronization phenomena are researched in various fields[1], [2]. The synchronization phenomenon can be observed on coupled oscillators system [3]. We are investigating the synchronization phenomena on coupled oscillators system, and are developing some systems using synchronization phenomena.In our previous study, we observed synchronization phenomena on the ladder shape systems and lattice shape systems. On the ladder shape systems, the phase-waves, which are phenomena of propagating a phase difference between adjacent oscillators, and the phase-inversion waves, which is a phenomenon of propagating a phase state between adjacent oscillators, were discovered. The propagation and reflection mechanisms of the phase-waves and the phase-inversion waves were clarified[4], [5]. On the lattice shape system, the phasewaves and the phase-inversion waves were discovered[6], [7]. Propagation and reflection mechanisms of the phase-waves were clarified [6]. Moreover, we developed a prediction method of time-series data using the lattice shape system. The timeseries data of Chua's circuit was predicted by this system [8].In this study, we clarify propagation mechanisms of the phase-inversion wave using instantaneous frequency of each oscillator and phase differences between adjacent oscillators on the lattice shape system. Furthermore, the air temperature data is predicted by the lattice shape system. The air temperature data is one of many natural data.