We have recently developed a mathematical model of axonal length sensing in which a system of delay differential equations describe a chemical signaling network. We showed that chemical oscillations emerge due to delayed negative feedback via a Hopf bifurcation, resulting in a frequency that is a monotonically decreasing function of axonal length. In this paper, we explore how frequency-encodin...

Population biologists have long been interested in the oscillations in population size displayed by many organisms in the field and laboratory. A wide range of deterministic mathematical models predict that these fluctuations can be generated internally by nonlinear interactions among species and, if correct, would provide important insights for understanding and predicting the dynamics of inte...

In this study, some techniques for the control of chaotic nonlinear systems with periodic coefficients are presented. First, chaos is eliminated from a given range of the system parameters by driving the system to a desired periodic orbit or to a fixed point using a full-state feedback. One has to deal with the same mathematical problem in the event when an autonomous system exhibiting chaos is...

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive ...

Seasonality strongly affects the transmission and spatio-temporal dynamics of many infectious diseases, and is often an important cause for their recurrence. However, there are many open questions regarding the intricate relationship between seasonality and the complex dynamics of infectious diseases it gives rise to. For example, in the analysis of long-term time-series of childhood diseases, ...

in recent years, mathematics is an essential aspect of all areas of daily life and the best predictor of being successful in economic situations of society. for many students, the mathematics accompanied with frustration, anxiety and negative attitudes towards mathematics. these students believe their anxiety have been derived from their math teachers, math misconception and weakness in math as...

Yansheng Liu1 and Donal O’Regan2 1 Department of Mathematics, Shandong Normal University, Jinan 250014, China 2 Department of Mathematics, National University of Ireland, Galway, Ireland Correspondence should be addressed to Yansheng Liu, [email protected] Received 13 March 2009; Accepted 12 April 2009 Recommended by Juan J. Nieto By using bifurcation techniques, this paper investigates the ex...

So-called ∗-autonomous, or “Frobenius”, category structures occur widely in mathematical quantum theory. This trend was observed in [3], mainly in relation to Hopf algebroids, and continued in [8] with a general account of Frobenius monoids. Below we list some of the ∗-autonomous partially ordered sets A = (A , p, j, S) that appear in the literature, an abstract definition of ∗-autonomous promo...

In this paper, a mathematical model of a prey-predator system is proposed to resolve the paradox of enrichment in ecosystems. The model is based on the natural strategy that a predator takes, i.e, it produces resting eggs in harsh environment. Our result gives a criterion for a functional response, which ensures that entering dormancy stabilizes the population dynamics. It is also shown that th...

This paper explains the implications of a mathematical theory (by the same authors) of holes in fractals and their relation to dimension for measurements. The novelty of our approach is to consider the fractal measure on a set rather than just the support of that measure. This should take into account in a more precise way the distribution of data points in measured sets, such as the distributi...