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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 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)


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)


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 p-adic behaviour of dynamical systems.

Stany De Smedt, Andrew Khrennikov (1999)

Revista Matemática Complutense

We study dynamical systems in the non-Archimedean number fields (i.e. fields with non-Archimedean valuation). The main results are obtained for the fields of p-adic numbers and complex p-adic numbers. Already the simplest p-adic dynamical systems have a very rich structure. There exist attractors, Siegel disks and cycles. There also appear new structures such as fuzzy cycles. A prime number p plays the role of parameter of a dynamical system. The behavior of the iterations depends on this parameter...

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