Incomplete synchronization of chaos under frequency-limited coupling: Observations in single-transistor microwave oscillators

Abstract

The synchronization of chaotic systems has been extensively studied based on diverse coupling schemes and media which allow almost unaltered energy exchange over the entire spectral range of oscillation. Less is known about the dynamics of systems encompassing couplings that restrict interaction to a narrower frequency interval, such as through band-pass filtering. Here, this situation is systematically investigated in the context of a master–slave pair of single-transistor chaotic oscillators operating in the microwave region. Albeit incomplete, phase synchronization remains detectable down to a fractional bandwidth on the order of 5% when the pass band is centered around the predominant spectral peaks, leading to a well-evident directed causal influence alongside intricate spectral effects. Concordant results are obtained between numerical simulations using an LC network and experimental measurements based on an electrically-tunable filter as a coupling medium. The possibility of maintaining selective locking over a channel shared between two oscillator pairs is shown. It is furthermore demonstrated that, in this circuit, frequency-limited coupling entrains one aspect of the chaotic dynamics, namely damped resonance, without significantly impacting the relaxation process that irregularly excites it. These results demonstrate in a realistic setting that chaos synchronization does not unavoidably require broadband couplings, thus enabling future applications of chaos communication using realistic antennas such as in distributed sensing. Some considerations about the construction of a hypothetical cellular network based on the coupling scheme under consideration are given.