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Drift, draft and structure: some mathematical models of evolution

Alison M. Etheridge (2008)

Banach Center Publications

Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to classical...

Drive network to a desired orbit by pinning control

Quanjun Wu, Hua Zhang (2015)

Kybernetika

The primary objective of the present paper is to develop an approach for analyzing pinning synchronization stability in a complex delayed dynamical network with directed coupling. Some simple yet generic criteria for pinning such coupled network are derived analytically. Compared with some existing works, the primary contribution is that the synchronization manifold could be chosen as a weighted average of all the nodes states in the network for the sake of practical control tactics, which displays...

Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling

G. A. Koch-Noble (2011)

Mathematical Modelling of Natural Phenomena

Pharmacokinetics is an excellent way to introduce biomathematical modeling at the sophomore level. Students have the opportunity to develop a mathematical model of a biological phenomenon to which they all can relate. Exploring pharmacokinetics takes students through the necessary stages of mathematical modeling: determining the goals of the model, deciphering between the biological aspects to include in the model, defining the assumptions of the model, and finally, building, analyzing, using, and...

Dürer polyhedra: the dark side of melancholia

Patrick W. Fowler, Peter E. John (2002)

Discussiones Mathematicae Graph Theory

Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible with the visible patch. Construction of all cubic polyhedra compatible with the visible portion (i.e., Dürer Polyhedra) is discussed, explicit graphs and symmetries are listed for small cases ( ≤ 18...

Dynamic external force feedback loop control of a robot manipulator using a neural compensator - Application to the trajectory following in an unknown environment

Farid Ferguene, Redouane Toumi (2009)

International Journal of Applied Mathematics and Computer Science

Force/position control strategies provide an effective framework to deal with tasks involving interaction with the environment. One of these strategies proposed in the literature is external force feedback loop control. It fully employs the available sensor measurements by operating the control action in a full dimensional space without using selection matrices. The performance of this control strategy is affected by uncertainties in both the robot dynamic model and environment stiffness. The purpose...

Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas

Jacek Waniewski, Wojciech Jędruch, Norbert Żołek (2004)

International Journal of Applied Mathematics and Computer Science

Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the...

Dynamical behavior of Volterra model with mutual interference concerning IPM

Yujuan Zhang, Bing Liu, Lansun Chen (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A Volterra model with mutual interference concerning integrated pest management is proposed and analyzed. By using Floquet theorem and small amplitude perturbation method and comparison theorem, we show the existence of a globally asymptotically stable pest-eradication periodic solution. Further, we prove that when the stability of pest-eradication periodic solution is lost, the system is permanent and there exists a locally stable positive periodic solution which arises from the pest-eradication...

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