The experimental setup.

<p>(a) The experimental equipment and the CCD acquisition system. (b) The details of the experimental equipment.</p

The experimental results.

<p>For <i>f</i>₁₀ = 158.47 BPM and <i>f</i>₂₀ = 156.52 BPM, we present (a) the time evolutions of <i>ϕ</i>_1,2, where envelopes of <i>ϕ</i>_1,2 exhibit anti-phase synchronization; (b) the phase trajectory in the </p><p></p><p></p><p><mo>(</mo><mi>ϕ</mi><mo>,</mo></p><p><mi>ϕ</mi><mo>˙</mo></p><mo>)</mo><p></p><p></p><p></p> space; and (c) the Poincaré maps. (d) The variation of the phase-locking ratio, <i>r</i>, as a function of the natural frequency of the second metronome, <i>f</i>₂₀. The arrow denotes the point at which <i>r</i> = <i>π</i> / 3.1.<p></p

A schematic illustration of the simplified model.

<p>A schematic illustration of the simplified model.</p

The numerical results.

<p>(a) The variation in the ratio of the working frequencies, <i>r</i>′ = <i>f</i>₁ / <i>f</i>₂, as a function of <i>f</i>₂₀ for <i>f</i>₁₀ = 160 BPM. As a reference, the ratio of the natural frequencies, <i>r</i>₀ = <i>f</i>₁₀ / <i>f</i>₂₀, is also plotted. (b) The variations in the working frequencies, <i>f</i>_1,2, as functions of <i>f</i>₂₀. Resonance-like behavior is observed in the region <i>f</i>₂₀ ∊ [160 − 2.4,160 + 2.4]. (c) The variations in the Lyapunov exponents, <i>λ</i>_1,2,3, as functions of <i>f</i>₂₀. At <i>f</i>₂₀ = 157.08915, the working frequencies are locked into the ratio <i>r</i>′ = <i>π</i> / 3.1, and the largest Lyapunov exponent is <i>λ</i>₁ ≈ 0.001.</p