59 research outputs found
Awakened oscillations in coupled consumer-resource pairs
The paper concerns two interacting consumer-resource pairs based on
chemostat-like equations under the assumption that the dynamics of the resource
is considerably slower than that of the consumer. The presence of two different
time scales enables to carry out a fairly complete analysis of the problem.
This is done by treating consumers and resources in the coupled system as
fast-scale and slow-scale variables respectively and subsequently considering
developments in phase planes of these variables, fast and slow, as if they are
independent. When uncoupled, each pair has unique asymptotically stable steady
state and no self-sustained oscillatory behavior (although damped oscillations
about the equilibrium are admitted). When the consumer-resource pairs are
weakly coupled through direct reciprocal inhibition of consumers, the whole
system exhibits self-sustained relaxation oscillations with a period that can
be significantly longer than intrinsic relaxation time of either pair. It is
shown that the model equations adequately describe locally linked
consumer-resource systems of quite different nature: living populations under
interspecific interference competition and lasers coupled via their cavity
losses.Comment: 31 pages, 8 figures 2 tables, 48 reference
A superconducting microwave multivibrator produced by coherent feedback
We investigate a coherent nonlinear feedback circuit constructed from
pre-existing superconducting microwave devices. The network exhibits emergent
bistable and astable states, and we demonstrate its operation as a latch and
the frequency locking of its oscillations. While the network is tedious to
model by hand, our observations agree quite well with the semiclassical
dynamical model produced by a new software package [N. Tezak et al.,
arXiv:1111.3081v1] that systematically interpreted an idealized schematic of
the system as a quantum optic feedback network.Comment: 9 double-spaced pages, 5 figures and supplement. To appear in Phys.
Rev. Let
Analog Realization of Arbitrary One-Dimensional Maps
An increasing number of applications of a one-dimensional (1-D) map as an information processing element are found in the literature on artificial neural networks, image processing systems, and secure communication systems. In search of an efficient hardware implementation of a 1-D map, we discovered that the bifurcating neuron (BN), which was introduced elsewhere as a mathematical model of a biological neuron under the influence of an external sinusoidal signal, could provide a compact solution. The original work on the BN indicated that its firing time sequence, when it was subject to a sinusoidal driving signal, was related to the sine-circle map, suggesting that the BN can compute the sine-circle map. Despite its rich array of dynamical properties, the mathematical description of the BN is simple enough to lend itself to a compact circuit implementation. In this paper, we generalize the original work and show that the computational power of the BN can be extended to compute an arbitrary 1-D map. Also, we describe two possible circuit models of the BN: the programmable unijunction transistor oscillator neuron, which was introduced in the original work as a circuit model of the BN, and the integrated-circuit relaxation oscillator neuron (IRON), which was developed for more precise modeling of the BN. To demonstrate the computational power of the BN, we use the IRON to generate the bifurcation diagrams of the sine-circle map, the logistic map, as well as the tent map, and then compare them with exact numerical versions. The programming of the BN to compute an arbitrary map can be done simply by changing the waveform of the driving signal, which is given to the BN externally; this feature makes the circuit models of the BN especially useful in the circuit implementation of a network of 1-D maps
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