Exploiting nonlinear dynamics in a coupled-core fluxgate magnetometer

Abstract

Unforced bistable dynamical systems having dynamics of the general form cannot oscillate (i.e. switch between their stable attractors). However, a number of such systems subject to carefully crafted coupling schemes have been shown to exhibit oscillatory behavior under carefully chosen operating conditions. This behavior, in turn, affords a new mechanism for the detection and quantification of target signals having magnitude far smaller than the energy barrier height in the potential energy function U(x) for a single (uncoupled) element. The coupling-induced oscillations are a feature that appears to be universal in systems described by bi- or multi-stable potential energy functions U(x), and are being exploited in a new class of dynamical sensors being developed by us. In this work we describe one of these devices, a coupled-core fluxgate magnetometer (CCFM), whose operation is underpinned by this dynamic behavior. We provide an overview of the underlying dynamics and, also, quantify the performance of our test device; in particular, we provide a quantitative performance comparison to a conventional (single-core) fluxgate magnetometer via a ‘resolution’ parameter that embodies the device sensitivity (the slope of its input–output transfer characteristic) as well as the noise floor.

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

“…Then either their difference or ratio can be used to quantify the signal. The sensitivity of this residence times distribution (RTD) based readout has been shown [8] to increase with lowered bias frequency and amplitude. These conditions are the opposite of the requirements for enhancing sensitivity in traditional (second harmonic) readouts, so that lower onboard power as well as far simpler electronics can be implemented, with benefit, for this (time domain based) readout strategy [8].…”

“…In recent works [4,5], we have demonstrated, theoretically and experimentally, that coupling similar bistable systems can lead, under certain conditions, to self-induced oscillations that mimic the hysteresis loop of a single element. The conditions depend, mainly, on the topology of connections and the number of units.…”

“…In Section 3 we provide a description of the dynamics of the coupled bistable model equation for a CCFM without delay, comprised of an odd number N of wound ferromagnetic cores. We note that N (unless taken to be quite large) must be odd [4,8]. Then in Section 4 we present results of an analytic and computational study of the effects of time delay.…”

A Hamiltonian approach to model and analyse networks of nonlinear oscillators: Applications to gyroscopes and energy harvesters

“…A direct calculation shows that the system in (15) is Hamiltonian with respect to the symplectic structure (5). The corresponding Hamiltonian is…”

“…Nowadays, integrable systems arise naturally at various length scales: in molecular dynamics [3], underwater vehicle dynamics [4], in magnetic-and electric-field sensors [5][6][7][8], hydroelastic rotating systems and boats/ships [9][10][11][12], in complex systems such as telecommunication infrastructures [13], and in power grids [14]. In this manuscript we present a review of the analysis of two seemingly unrelated arrays of N mechanical systems: one of vibratory gyroscopes [12,[15][16][17] and the other of energy harvester devices [18,19].…”