Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 496, Issue 2, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2020.124840
Keywords
Gray-Scott model; Cubic polynomial system; Phase portraits; Bifurcation diagram; Hopf bifurcation
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Funding
- National Natural Science Foundation of China [12071091, 11661017, 12001112, 11771059]
- Science and Technology Program of Guangzhou [201804010350]
- Natural Science Foundation of Guangdong Province [2019A1515011885]
- Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigacion [MTM2016-77278-P]
- Agencia de Gestio d'Ajuts Universitaris i de Recerca grant [2017SGR1617]
- H2020 European Research Council [MSCA-RISE-2017-777911]
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The paper gives a complete classification of the phase portraits of cubic polynomial systems in the Poincare disk, corresponding to the Gray-Scott model, based on the values of parameters a and b. Additionally, a bifurcation diagram in the parameter plane (a, b) of these systems is provided.
We give a complete classification of the phase portraits in the Poincare disk for the cubic polynomial systems (x) over dot = 1 - x - axy(2), (y) over dot = -by + axy(2), in R-2 according with the values of its two parameters a and b. These differential systems correspond to the Gray-Scott model. Moreover we provide the bifurcation diagram in the parameter plane (a, b) of these systems. (C) 2020 Elsevier Inc. All rights reserved.
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