Complex behavior in driven unidirectionally coupled overdamped Duffing elements

Abstract

It is well known that overdamped unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations (corresponding to transitions between the stable steady states of each nonlinear element) when a control parameter exceeds a threshold value. In recent publications [A. Bulsara, Phys. Rev. E 70, 036103 (2004); V. In, ibid. 72, 045104 (2005)], we demonstrated this behavior in a specific prototype system, a soft-potential mean-field description of the dynamics in a hysteretic "single-domain" ferromagnetic sample. These oscillations are now finding utility in the detection of very weak "target" magnetic signals, via their effect on the oscillation characteristics--e.g., the frequency and asymmetry of the oscillation wave forms. We explore the underlying dynamics of a related system, coupled bistable "standard quartic" dynamic elements; the system shows similarities to, but also significant differences from, our earlier work. dc as well as time-periodic target signals are considered; the latter are shown to induce complex oscillatory behavior in different regimes of the parameter space. In turn, this behavior can be harnessed to quantify the target signal.

Basins of attraction in a ring of overdamped bistable systems with delayed coupling

“…But, more importantly, since the oscillations appear without the need of an external signal, they provide an alternative signal detection scheme as well as, potentially, enhanced sensitivity. These results have been incorporated into a "coupled core fluxgate magnetometer (CCFM)" [4] and in a "coupled electric field sensor (CEFS)" [6]. The analysis of the effects of different coupling schemes has also led to the prediction of novel cooperative behavior in a ring of coupled SQUID (Superconducting Quantum Intereference Devices) devices [7].…”

Effects of charge collectors in ferroelectric E-field sensors

“…The theoretical treatment has been supported by experimental results confirming the suitability of the methodology proposed. A nonlinear dynamical system based on ferroelectric capacitors coupled into a unidirectional ring circuit which under particular conditions exhibits an oscillating regime of behavior [13], is considered in this paper with particular interest for developing novel E-field sensors. Preliminary results showing the suitability of such a circuit to detect external E-fields have been presented in [14].…”

“…Instruments for E-field measurements (e.g., body and ground reference meters, electro-optic meters, the Kelvin probe and shutter-and cylindrical-type field mills) are generally based on linear transduction mechanisms. In recent works [1], [13]- [16], the authors have presented the idea of innovative Efield sensing solutions based on nonlinear coupled oscillators with hysteretic elements. In particular, in [1] a single non linear dynamic device employing a ferroelectric capacitor to measure quasi-static E-fields has been discussed.…”

Symmetry-Breaking as a Paradigm to Design Highly-Sensitive Sensor Systems

“…One realizes, immediately, that the dynamics of the system (11) are likely to be quite different from the magnetic sensors discussed in Section 3.1 because of the differences in the (inter-element, as well as external signal) coupling mechanisms. A bifurcation analysis [5] reveals that the system (11) exhibits oscillatory behavior with the following features:…”

“…The oscillations emerge through a global branch of heteroclinic connections between steady states, so that near the onset of the cycle, the accompanying oscillations exhibit long periods, which in turn renders their waveform highly sensitive to symmetry-breaking effects caused by very small external signals. This critical observation has led to the fabrication of highly-sensitive sensors, magnetic-and electric-field ones, whose operation relies mainly on the coupling signal that travels from one bistable system to the next one [3][4][5][6]. That is, in the absence of coupling, each bistable unit cannot oscillate.…”