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We study a reaction-diffusion equation
with an integral term describing nonlocal consumption of resources
in population dynamics. We show that a homogeneous equilibrium can
lose its stability resulting in appearance of stationary spatial
structures. They can be related to the emergence of biological
species due to the intra-specific competition and random
mutations.
Various types of travelling waves are observed.
One of the most intriguing questions in life science is how living organisms develop and maintain their predominant form and shape via the cascade of the processes of differentiation starting from the single cell. Mathematical modeling of these developmental processes could be a very important tool to properly describe the complex processes of evolution and geometry of morphogenesis in time and space. Here, we summarize the most important biological knowledge on plant development, exploring the...
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