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Patterns, Memory and Periodicity in Two-Neuron Delayed Recurrent Inhibitory Loops

J. Ma, J. Wu (2010)

Mathematical Modelling of Natural Phenomena

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...

Patterns of Zooplankton Functional Response in Communities with Vertical Heterogeneity: a Model Study

A. Morozov, E. Arashkevich (2008)

Mathematical Modelling of Natural Phenomena

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...

Positive and Negative Feedback in Engineering and Biology

E. S. Zeron (2008)

Mathematical Modelling of Natural Phenomena

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....

Positive fixed point theorems arising from seeking steady states of neural networks

Gen Qiang Wang, Sui-Sun Cheng (2010)

Mathematica Bohemica

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...

Possibly Longest Food Chain: Analysis of a Mathematical Model

T. Matsuoka, H. Seno (2008)

Mathematical Modelling of Natural Phenomena

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,...

Pre-symptomatic Influenza Transmission, Surveillance, and School Closings: Implications for Novel Influenza A (H1N1)

G. F. Webb, Y-H. Hsieh, J. Wu, M. J. Blaser (2010)

Mathematical Modelling of Natural Phenomena

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...

Reaction-Diffusion Modelling of Interferon Distribution in Secondary Lymphoid Organs

G. Bocharov, A. Danilov, Yu. Vassilevski, G.I. Marchuk, V.A. Chereshnev, B. Ludewig (2011)

Mathematical Modelling of Natural Phenomena

This paper proposes a quantitative model of the reaction-diffusion type to examine the distribution of interferon-α (IFNα) in a lymph node (LN). The numerical treatment of the model is based on using an original unstructured mesh generation software Ani3D and nonlinear finite volume method for diffusion equations. The study results in suggestion that due to the variations in hydraulic conductivity of various zones of the secondary lymphoid organs...

Reconstruction and Quantification of Diffusion Tensor Imaging-Derived Cardiac Fibre and Sheet Structure in Ventricular Regions used in Studies of Excitation Propagation

A. P. Benson, S. H. Gilbert, P. Li, S. M. Newton, A. V. Holden (2008)

Mathematical Modelling of Natural Phenomena

Detailed descriptions of cardiac geometry and architecture are necessary for examining and understanding structural changes to the myocardium that are the result of pathologies, for interpreting the results of experimental studies of propagation, and for use as a three-dimensional orthotropically anisotropic model for the computational reconstruction of propagation during arrhythmias. Diffusion tensor imaging (DTI) provides a means to reconstruct fibre and sheet orientation throughout the ventricles....

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