Spatiotemporal synchronization patterns in large arrays of coupled triode-based van der Pol oscillators

Abstract

Abstract A common way to improve a beam-steering system based on a coupled oscillator array is to increase the number of oscillators to boost power, improve focus and resolution, and enhance steering precision. This study deals with the numerical analysis of the spatiotemporal dynamics of a network of N > 4 coupled triode-based van der Pol oscillator arrays for beam steering application, extending from a previous study in which the dynamics of N ≤ 4 coupled oscillators were successfully evaluated as phase shifters for electronic beam steering, achieving significant phase shifts and high-power outputs at ultrasonic frequencies. We create a comprehensive map of the different collective dynamic behaviors across different oscillating units in terms of the coupling strength and edge oscillator frequency. In addition to full synchronization, traveling waves, and oscillations death reported in the previous study, simulations reveal new patterns such as cluster traveling wave and ‘imperfect’ intermittent traveling wave as transitions between traveling waves and cluster state. Furthermore, the findings reveal that in addition to the emergence of new spatiotemporal patterns, the maximal phase shift decreases as the number of oscillators increases. For parameter settings in the beam steering region, the output waveform is applied as the input signal for linear phased array transducers. The results of the variation of the array aperture width show that the sound pressure peaks in the steered direction, while beam directivity improves with wider apertures. These results are in agreement with LTSPICE simulations and provide an alternative way to design high-power coupled oscillator arrays for beam steering applications.