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Recent technological advances including brain imaging (higher resolution in space and
time), miniaturization of integrated circuits (nanotechnologies), and acceleration of
computation speed (Moore’s Law), combined with interpenetration between neuroscience,
mathematics, and physics have led to the development of more biologically plausible
computational models and novel therapeutic strategies. Today, mathematical models of
irreversible medical conditions...
We study the coexistence of multiple periodic solutions for an analogue of the
integrate-and-fire neuron model of two-neuron recurrent inhibitory loops with delayed
feedback, which incorporates the firing process and absolute refractory period. Upon
receiving an excitatory signal from the excitatory neuron, the inhibitory neuron emits a
spike with a pattern-related delay, in addition to the synaptic delay. We present a
theoretical framework to view...
Parameterization of zooplankton functional response is crucial for constructing plankton models. Theoretical
studies predict enhancing of system stability in case the response is of sigmoid type. Experiments on feeding in laboratories tell us in
favor of non-sigmoid types for most herbivorous zooplankton species. However, recent field observations show that the overall functional
response of zooplankton in the whole euphotic zone can exhibit a sigmoid behavior even when the response for the same...
No other concepts have shaken so deeply the bases of engineering like those of positive
and negative feedback. They have played a most prominent role in engineering since the beginning
of the previous century. The birth certificate of positive feedback can be traced back to a pair of
patents by Edwin H. Armstrong in 1914 and 1922, whereas that of negative feedback is already
lost in time. We present in this paper a short review on the feedback's origins in the fields of
engineering and biology....
Biological systems are able to switch their neural systems into inhibitory states and it is therefore important to build mathematical models that can explain such phenomena. If we interpret such inhibitory modes as `positive' or `negative' steady states of neural networks, then we will need to find the corresponding fixed points. This paper shows positive fixed point theorems for a particular class of cellular neural networks whose neuron units are placed at the vertices of a regular polygon. The...
We consider the number of trophic levels in a food chain given by the
equilibrium state for a simple mathematical model with ordinary differential
equations which govern the temporal variation of the energy reserve in each
trophic level. When a new trophic level invades over the top of the chain,
the chain could lengthen by one trophic level.
We can derive the condition that such lengthening could
occur, and prove that the possibly longest chain is globally stable.
In some specific cases,...
Early studies of the novel swine-origin 2009 influenza A (H1N1) epidemic indicate
clinical attack rates in children much higher than in adults. Non-medical interventions
such as school closings are constrained by their large socio-economic costs. Here we
develop a mathematical model to ascertain the roles of pre-symptomatic influenza
transmission as well as symptoms surveillance of children to assess the utility of school
closures. Our model analysis...
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