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Temporally Interruptive Interaction Allows Mutual Invasion of Two Competing Species Dispersing in Space

Hiromi Seno (2010)

Mathematical Modelling of Natural Phenomena

With a reaction-diffusion system, we consider the dispersing two-species Lotka-Volterra model with a temporally periodic interruption of the interspecific competitive relationship. We assume that the competition coefficient becomes a given positive constant and zero by turns periodically in time. We investigate the condition for the coexistence of two competing species in space, especially in the bistable case for the population dynamics without dispersion. We could find that the spatial coexistence,...

The Effect of Bacteria on Epidermal Wound Healing

E. Agyingi, S. Maggelakis, D. Ross (2010)

Mathematical Modelling of Natural Phenomena

Epidermal wound healing is a complex process that repairs injured tissue. The complexity of this process increases when bacteria are present in a wound; the bacteria interaction determines whether infection sets in. Because of underlying physiological problems infected wounds do not follow the normal healing pattern. In this paper we present a mathematical model of the healing of both infected and uninfected wounds. At the core of our model is an...

The formation of a tree leaf

Qinglan Xia (2007)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, we build a mathematical model to understand the formation of a tree leaf. Our model is based on the idea that a leaf tends to maximize internal efficiency by developing an efficient transport system for transporting water and nutrients. The meaning of “the efficient transport system” may vary as the type of the tree leave varies. In this article, we will demonstrate that tree leaves have different shapes and venation patterns mainly because they have adopted different efficient...

The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology

H. G. Othmer, K. Painter, D. Umulis, C. Xue (2009)

Mathematical Modelling of Natural Phenomena

We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding...

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