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Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel

M. Neamţu, L. Buliga, F. R. Horhat, D. Opriş (2010)

Mathematical Modelling of Natural Phenomena

The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematical models of infectious diseases it is important to predict whether the infection disappears or the pathogens persist. The delay kernel is described by the memory function that reflects the influence of the past density of pathogen in the blood and it is given by a nonnegative bounded and normated function k defined...

Hopf bifurcation analysis of some hyperchaotic systems with time-delay controllers

Lan Zhang, Cheng Jian Zhang (2008)

Kybernetika

A four-dimensional hyperchaotic Lü system with multiple time-delay controllers is considered in this paper. Based on the theory of Hopf bifurcation in delay system, we obtain a simple relationship between the parameters when the system has a periodic solution. Numerical simulations show that the assumption is a rational condition, choosing parameter in the determined region can control hyperchaotic Lü system well, the chaotic state is transformed to the periodic orbit. Finally, we consider the differences...

Hopf's ratio ergodic theorem by inducing

Roland Zweimüller (2004)

Colloquium Mathematicae

We present a very quick and easy proof of the classical Stepanov-Hopf ratio ergodic theorem, deriving it from Birkhoff's ergodic theorem by a simple inducing argument.

Hubbard trees

Alfredo Poirier (2010)

Fundamenta Mathematicae

We provide a full classification of postcritically finite polynomials as dynamical systems by means of Hubbard trees. The information encoded in these objects is solid enough to allow us recover all the relevant statical and dynamical aspects of the corresponding Julia sets.

Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling

G. Bocharov, V. Chereshnev, I. Gainova, S. Bazhan, B. Bachmetyev, J. Argilaguet, J. Martinez, A. Meyerhans (2012)

Mathematical Modelling of Natural Phenomena

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally disrupted? (ii)...

Hybrid matrix models and their population dynamic consequences

Sanyi Tang (2003)

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

In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation as well...

Currently displaying 1921 – 1940 of 4754