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A beginner's guide to adaptive dynamics

Odo Diekmann (2003)

Banach Center Publications

The aim of these notes is to illustrate, largely by way of examples, how standard ecological models can be put into an evolutionary perspective in order to gain insight in the role of natural selection in shaping life history characteristics. We limit ourselves to phenotypic evolution under clonal reproduction (that is, we simply ignore the importance of genes and sex). Another basic assumption is that mutation occurs on a time scale which is long relative to the time scale of convergence...

A continuum of path-dependent equilibrium solutions induced by sticky expectations

Pavel Krejčí, Eyram Kwame, Harbir Lamba, Dmitrii Rachinskii, Andrei Zagvozdkin (2023)

Applications of Mathematics

We analyze a simple macroeconomic model where rational inflation expectations are replaced by a boundedly rational, and genuinely sticky, response to changes in the actual inflation rate. The stickiness is introduced in a novel way using a mathematical operator that is amenable to rigorous analysis. We prove that, when exogenous noise is absent from the system, the unique equilibrium of the rational expectations model is replaced by an entire line segment of possible equilibria with the one chosen...

A Cost-Effectiveness-Assessing Model of Vaccination for Varicella and Zoster

M. Comba, S. Martorano-Raimundo, E. Venturino (2012)

Mathematical Modelling of Natural Phenomena

A decision analytical model is presented and analysed to assess the effectiveness and cost-effectiveness of routine vaccination against varicella and herpes-zoster, or shingles. These diseases have as common aetiological agent the varicella-zoster virus (VZV). Zoster can more likely occur in aged people with declining cell-mediated immunity. The general concern is that universal varicella vaccination might lead to more cases of zoster: with more...

A model of cardiac tissue as an excitable medium with two interacting pacemakers having refractory time

Alexander Loskutov, Sergei Rybalko, Ekaterina Zhuchkova (2003)

Banach Center Publications

A quite general model of the nonlinear interaction of two impulse systems describing some types of cardiac arrhythmias is developed. Taking into account a refractory time the phase locking phenomena are investigated. Effects of the tongue splitting and their interweaving in the parametric space are found. The results obtained allow us to predict the behavior of excitable systems with two pacemakers depending on the type and intensity of their interaction and the initial phase.

A new approach to generalized chaos synchronization based on the stability of the error system

Zhi Liang Zhu, Shuping Li, Hai Yu (2008)

Kybernetika

With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity....

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

Saleh Mobayen, Fairouz Tchier (2015)

Kybernetika

This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained...

A New Mathematical Model of Syphilis

F. A. Milner, R. Zhao (2010)

Mathematical Modelling of Natural Phenomena

The CDC launched the National Plan to Eliminate Syphilis from the USA in October 1999 [4]. In order to reach this goal, a good understanding of the transmission dynamics of the disease is necessary. Based on a SIRS model Breban et al.  [3] provided some evidence that supports the feasibility of the plan proving that no recurring outbreaks should occur for syphilis. We study in this work a syphilis model that includes partial...

A non-linear discrete-time dynamical system related to epidemic SISI model

Sobirjon K. Shoyimardonov (2021)

Communications in Mathematics

We consider SISI epidemic model with discrete-time. The crucial point of this model is that an individual can be infected twice. This non-linear evolution operator depends on seven parameters and we assume that the population size under consideration is constant, so death rate is the same with birth rate per unit time. Reducing to quadratic stochastic operator (QSO) we study the dynamical system of the SISI model.

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