Biomedical subjects
F C Hoppensteadt
Publications and source records attributed to F C Hoppensteadt.
Intermittent chaos, self-organization, and learning from synchronous synaptic activity in model neuron networks.
Self-organization of frequencies is studied by using model neurons called VCONs (voltage-controlled oscillator neuron models). These models give direct access to frequency information, in contrast to all-or-none neuron models, and they generate voltage spikes that phase-lock to oscillatory stimulation, similar to phase-locking of action potentials to oscillatory voltage stimulation observed in Hodgkin-Huxley preparations of squid axons. The rotation vector method is described and used to study how networks synchronize, even in the presence of noise or when damaged; the entropy of ratios of phases is used to construct an energy function that characterizes organized behavior. Computer simulations show that rotation numbers (output frequency/input frequency) describe both chaotic and nonchaotic behavior. Learning occurs when synaptic connections strengthen in response to stimulation that is synchronous with cell activity. It is shown that intermittent chaotic firing is suppressed and simple stable responses are enhanced by such learning in VCON networks. This analysis provides a rigorous basis for further investigation of the ideas of Wiener [Wiener, N. (1961) Cybernetics (MIT Press, Cambridge, MA), p. 191] on the origin of slow brain waves due to "the pulling together of frequencies."
A mathematical analysis of small mammal populations.
Populations of Microtus montanus, the montane vole, have been extensively studied. It is known that their reproductive activity is closely linked to the availability of the chemicals in growing plants. We use a mathematical model here to study how the length of the vegetative season and the natural reproduction rhythm of voles are involved in the long term dynamics of the population numbers. In particular, we use data obtained from Timpie Springs, Utah, and from Jackson Hole, Wyoming, to formulate a model. The novelty of this model is its use of littering curves that highlight the temporally discrete nature of vole reproduction. The model shows how the timing of the vegetative season can influence vole population sizes.
Frequency modulation dynamics in neural networks.
The VCON model described here shares certain qualitative features of stimulus-response characteristics with the data in FIGURE 1 and TABLE 1. At the same time, it provides an uncomplicated methodology for modelling neural networks that emphasizes their frequency aspects. In particular, models based on VCONs are amenable to the rotation vector method, which can be used to uncover stable synchronization of firing within a network. This is described in the appendix, where it is shown that the stable firing patterns within the network correspond to minima of an associated (local) energy function. We have seen here how a model of a simple CPG for breathing can be constructed and analyzed. Similar models for rhythm splitting of small mammal activity cycles, sound location networks, and motility in the gastrointestinal tract have been constructed, and large networks of VCONs have been shown to have stable spatial patterns of synchronization.
On plasmid incompatibility.
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Synchronization of periodical cicada emergences.
Synchronized insect emergences are shown to be a possible consequence of predation in the presence of a limited environmental carrying capacity through a mathematical model for cicada populations that includes these two features. Synchronized emergences, like those observed in 13- and 17-year cicades, are predicted for insects with sufficiently long life-spans. Balanced solutions, in which comparable emergences occur each year, are found for insects having sufficiently short life-spans, such as 3-, 4-, and 7-year cicadas. For the values used here, synchronized emergences occur for insects with life-spans of 10 years or more, and balanced emergences occur for life-spans of fewer than 10 years.
A slow selection analysis of two locus, two allele traits.
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