Dynamics of species in a nonautonomous Lotka-Volterra system.
Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory
We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...
Dynamics of the tumor-immune system competition - the effect of time delay
The model analyzed in this paper is based on the model set forth by V.A. Kuznetsov and M.A. Taylor, which describes a competition between the tumor and immune cells. Kuznetsov and Taylor assumed that tumor-immune interactions can be described by a Michaelis-Menten function. In the present paper a simplified version of the Kuznetsov-Taylor model (where immune reactions are described by a bilinear term) is studied. On the other hand, the effect of time delay is taken into account in order to achieve...
Dynamics of Tuberculosis: The effect of Direct Observation Therapy Strategy (DOTS) in Nigeria
This paper presents mathematical models for tuberculosis and its dynamics under the implementation of the direct observation therapy strategy (DOTS) in Nigeria. The models establish conditions for the eradication of tuberculosis in Nigeria based on the fraction of detected infectious individuals placed under DOTS for treatment. Both numerical and qualitative analysis of the models were carried out and the effect of the fraction of detected cases of active TB on the various epidemiological classes...
Ecological modeling and Lagrangian approach
A mathematical model is proposed for a quantitative estimation of the damage to biological resources resulting from a pollutant discharge into an aqueous environment. On the basis of the Lagrangian description of fluid motion a set of hydrophysical parameters is introduced with help of which hydrobiologists can estimate the damage. The computation of parameters introduced is illustrated by the example of a model problem of a pollutant spreading in a canal. For the discretization of the problem a...
Edge of chaos in reaction diffusion CNN model
In this paper, we study the dynamics of a reaction-diffusion Cellular Nonlinear Network (RD-CNN) nodel in which the reaction term is represented by Brusselator cell. We investigate the RD-CNN dynamics by means of describing function method. Comparison with classical results for Brusselator equation is provided. Then we introduce a new RD-CNN model with memristor coupling, for which the edge of chaos regime in the parameter space is determined. Numerical simulations are presented for obtaining dynamic...
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Effect of allocated radiotherapy after breast surgeries over death risk in early breast cancer patients: a meta-analysis.
Effect of randomly fluctuating environment on autotroph-herbivore model system.
Effect of time delay on a detritus-based ecosystem.
Effect on persistence of intra-specific competition in competition models.
Effects of competition and predation in a three species model
A model which consists of a predator and two prey species is presented. The prey compete for the same limited resource (food). The predator preys on both prey species but with different severity. We show that the coexistence of all three species is possible in a mean-field approach, whereas from Monte Carlo simulation it follows that the stochastic fluctuations drive one of the prey populations into extinction.
Effects of Poiseuille flow on peristaltic transport.
Effects of small spatial variation of the reproduction rate in a two species competition model.
Ein dauerhaftes Zusammenleben zweier Populationen.
Einschliessungsaussagen bei Systemen semilinearer parabolischer Differentialgleichungen
Für die Lösungen seminlinearer parabolischer Differentialgleichungen werden Einschliessungsaussagen hergeleitet. Hierbei werden Aussagen zur Stabilität von Lösungen ermittelt. Die Resultate werden am Beispiel der Fitzhugh-Nagumo Gleichungen diskutiert.
Elektronický model neuronu podle N. I. Vvedenského
Emotion learning: Solving a shortest path problem in an arbitrary deterministic environment in linear time with an emotional agent
The paper presents an algorithm which solves the shortest path problem in an arbitrary deterministic environment with n states with an emotional agent in linear time. The algorithm originates from an algorithm which in exponential time solves the same problem, and the agent architecture used for solving the problem is an NN-CAA architecture (neural network crossbar adaptive array). By implementing emotion learning, the linear time algorithm is obtained and the agent architecture is modified. The...
Emotional learning based intelligent speed and position control applied to neurofuzzy model of switched reluctance motor
Enrichment Paradox Induced by Spatial Heterogeneity in a Phytoplankton - Zooplankton System
This paper is devoted to the study of a predator-prey model in a patchy environment. The model represents the interactions between phytoplankton and zooplankton in the water column. Two patches are considered with respect to light availability: one patch is associated to the surface layer, the second patch describes the bottom layer. We show that this spatial heterogeneity may destabilize the predator-prey system, even in oligotrophic system where the nutrient is low enough to avoid ”paradox-enrichment”...