No 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 when a control parameter exceeds a threshold value. In a recent publication [Phys. Rev. E 68, 045102 (2003)]], 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. The previous analysis of this work showed that N (odd) unidirectionally coupled elements with cyclic boundary conditions would, in fact, oscillate when a control parameter-in this case the coupling strength-exceeded a critical value. These oscillations are now finding utility in the detection of very weak "target" signals, via their effect on the oscillation characteristics, e.g., the frequency and asymmetry of the oscillation wave forms. In this paper we explore the underlying dynamics of this system. Scaling laws that govern the oscillation frequency in the vicinity of the critical point, as well as the zero-crossing intervals in the presence of a symmetry-breaking target dc signal, are derived; these quantities are germane to signal detection and analysis.

An analysis of stationary and nonstationary cellular patterns observed in premixed flames on a circular, porous plug burner is presented. A phenomenological model is introduced, that exhibits patterns similar to the experimental states. The primary modes of the model are combinations of Fourier-Bessel functions, whose radial parts have neighboring zeros. This observation explains several features of patterns, such as the existence of concentric rings of cells and the weak coupling between rings. Properties of rotating rings of cells, including the existence of modulated rotations and heteroclinic cycles can be deduced using mode coupling. For nonstationary patterns, the modal decomposition of experimental data can be carried out using the Karhunen-Loeve (KL) analysis. Experimental states are used to demonstrate the possibility of using KL analysis to differentiate between uniform and nonuniform rotations. The methodology can be extended to study more complicated nonstationary patterns. In particular, it is shown how the complexity of "hopping states" can be unraveled through the analysis. (c) 1997 American Institute of Physics.

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.

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.