Strong Coupling of Nonlinear Electronic and Biological Oscillators: Reaching the “Amplitude Death” Regime

Interaction between an electronic and a biological circuit has been investigated for a pair of electrically connected nonlinear oscillators, with a spontaneously oscillating olivary neuron as the single-cell biological element. By varying the coupling strength between the oscillators, we observe a range of behaviors predicted by model calculations, including a reversible low-energy dissipation “amplitude death” where the oscillations in the coupled system cease entirely.

Figure 1

(a) The electronic oscillator circuit with $R_1=R_2=10\mathrm{K}\Omega$, $R_3=35\mathrm{K}\Omega$, $R_4=100\mathrm{K}\Omega$, $C=100\mathrm{n}\mathrm{F}$, $L=250000\mathrm{H}$. (b) Schematic of the experimental arrangement. The box $A$ is an adjustable-gain amplifier to match the amplitudes of oscillations in electronic (typically 10–20 mV) and in biological (typically 5–15 mV) oscillators. Boxes $K_1$ and $K_2$ are also adjustable-gain amplifiers to determine different coupling coefficients.

Figure 2

Calculated bifurcation diagram for the coupled nonlinear olivary neuron-electronic oscillator pair, as a function of the coupling coefficients $K_1$ and $K_2$.

Figure 3

(a)–(c) Experimental results for the coupled system in the weak coupling (independent oscillators), medium coupling (synchronous oscillation; in and out of phase), and strong coupling (amplitude death) regimes, respectively. (d)–(f) Corresponding results from theory in the three regimes; the amplitude death regime is reached after a transient following step function increase in the coupling coefficients.

Figure 4

Computed return from amplitude death in the presence and the absence of a 1 mV rms noise, respectively.