In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the ...

In the preface we present a short overview of articles included in the issue “Bifurcations and pattern formation in biological applications” of the journal Mathematical Modelling of Natural Phenomena.

This paper is devoted to the existence and stability analysis of limit cycles in a delayed mathematical model for the economy growth. Specifically the Solow model is further improved by inserting the time delay into the logistic population growth rate. Moreover, by choosing the time delay as a bifurcation parameter, we prove that the system loses its stability and a Hopf bifurcation occurs when...

We study the patterns formed on ion sputtered Si surfaces as a function of ion energy and incidence angle, and identify a region in parameter space where the flat surface is stable. The boundaries between the stable and pattern-forming regions represent mathematical bifurcations. Our data set exhibits at least two different bifurcation types. We discuss the constraints imposed by these observat...

A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first t...

We construct a global bifurcation diagram of the plane differential system ẋ = x(1− x)− xy/(a+ x), ẏ = y(δ − βy/x), x(t) > 0, y(t) > 0, a > 0, δ > 0, β > 0, which describes the predator-prey interaction. In [1] was considered the following planar differential systems which describes a mathematical predator-prey model ẋ = rx(1 − x K )− mx b+x y, ẏ = sy(1− y hx ). (1) Here x(t) > 0, y(t) > 0 — th...

We show that numerous distinctive concepts of constructive mathematics arise automatically from an "antithesis" translation affine logic into intuitionistic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict non-strict order pairs, cut-valued metrics, spaces. also explain the bifurcation some classical using choice ...

We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (in Mathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the pheno...

"Mayer waves" are long-period (6 to 12 seconds) oscillations in arterial blood pressure, which have been observed and studied for more than 100 years in the cardiovascular system of humans and other mammals. A mathematical model of the human cardiovascular system is presented, incorporating parameters relevant to the onset of Mayer waves. The model is analyzed using methods of Liapunov stabilit...

In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-I type in the closed first quadrant 2  R . The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a NeimarkSacker bifurcation in the interior of 2  R by using bifurcation theory...