@article{
 title = {Transition of patterns in the cell-chemotaxis system with proliferation source},
 type = {article},
 year = {2015},
 identifiers = {[object Object]},
 keywords = {Cell-chemotaxis,Dynamic bifurcation,Hexagonal patterns,Phase transition},
 id = {31a465eb-e099-3f81-bd29-fbab277619c1},
 created = {2019-10-01T02:56:41.594Z},
 file_attached = {false},
 profile_id = {d8600050-807a-308a-bc20-15bcc721dbb4},
 last_modified = {2019-10-01T02:59:05.096Z},
 read = {false},
 starred = {false},
 authored = {true},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {Phase transition analysis is a fundamental component in understanding pattern-forming behavior of many biochemical systems, such as those found in developmental biology. The purpose of this work is to analyze the phase transition property of a diffusion-chemotaxis model with proliferation source, a macroscopic model of mobile species aggregation. Along the way, we will show that the system exhibits a very rich pattern-forming behavior, resulting in a competition between hexagonal, roll, and rectangular patterns. In particular, we show existence of regular hexagonal patterns in a confined spatial geometry where only two modes become unstable. It is also shown that they are either saddle points or attracting nodes. Moreover, we show that the competition happens inside a local attractor which consists of a finite number of stationary solutions and their connecting heteroclinic orbits. The structure of this attractor will be precisely determined as well.},
 bibtype = {article},
 author = {Yari, Masoud},
 journal = {Nonlinear Analysis, Theory, Methods and Applications}
}

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