Bistable systems are prevalently found in many sensor systems. It is well established that a well-designed coupling scheme, together with an appropriate choice of initial conditions, can induce oscillations (i.e. periodic switching between stable fixed points) in over-damped bistable dynamical systems when a control parameter exceeds a threshold value. This behavior was demonstrated in a specific prototype system comprised of three unidirectionally coupled ferromagnetic cores, the basis of a coupled core fluxgate magnetometer. Another prototypical (quartic potential based) system of coupled over-damped Duffing elements has been applied to describe the dynamics of the polarization inside a ferroelectric material, the basis of an electric-field sensor currently under development.

The analysis showed that N (odd) unidirectionally coupled elements with cyclic boundary conditions would oscillate when a control parameter (i.e. coupling strength) exceeded a critical value. Note that the oscillatory behavior can also be seen for large, even N. Typically, the oscillations emerge with an infinite period through a hetero-clinic-cycle bifurcation (i.e. a global bifurcation) to a collection of solution trajectories that connects sequences of equilibria and/or periodic solutions. In the particular case of overdamped bistable systems, the cycle includes mainly saddle-node equilibria. As a control parameter (usually the coupling strength) approaches from above a critical value, the frequency of the oscillations decreases, approaching zero at the critical point. Past the critical value, the oscillations disappear, and the system dynamics settles into an equilibrium.

The basin of attraction of the oscillations spans almost the entire phase space with the exception of a small region near the symmetrical initial conditions, in which case, the coupled system settles asymptotically to its stable fixed points. The emergent oscillations, in either the ferromagnetic or ferroelectric systems mentioned above, have been used to detect very weak “target” (dc and ac) signals via the (signal-induced) changes in the oscillation characteristics, e.g., duty cycle and frequency. It is important to emphasize that this emergent oscillatory behavior is quite general; in a non-sensor application, it has led to interesting frequency-selective properties of interacting neural networks.

The above phenomena open up new possibilities for the exploitation of a large class of (normally) non-oscillatory systems for a variety of practical applications that involve the use of the emergent self-sustained oscillations as a reference. The latest realization of a system in this class is an overdamped bistable system as one of the active elements in a microcircuit, which is intended to be used for measuring minute voltage or current changes that may be injected into the system.

Overall, the analysis and results of the microcircuit dynamics are in very good agreement with previous theoretical results. There are, however, important differences in the characteristic function and coupling function of the microcircuit device that can lead to far richer and more complex behavior in the detection of ac signals than in the theoretical models. For instance, additional branches of steady states and the

possibility of chaotic behavior in the microcircuit are possible.

This work was done by Visarath In, Patrick Longhini, Norman Liu, Andy Kho, Joseph D. Neff, and Adi R. Bulsara of the Space and Naval Warfare Systems Center; and Antonio Palacios of San Diego State University. For more information, download the Technical Support Package (free white paper) at under the Electronics/Computers category. NRL-0041

This Brief includes a Technical Support Package (TSP).
A Bistable Microelectronic Circuit for Sensing an Extremely Low Electric Field

(reference NRL-0041) is currently available for download from the TSP library.

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This article first appeared in the June, 2010 issue of Defense Tech Briefs Magazine.

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