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Dynamics of an autocatalator model
Author(s) -
Romanovski Valery G.,
Han Maoan,
Maćešić Stevan,
Tang Yilei
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4949
Subject(s) - mathematics , ordinary differential equation , dynamics (music) , equilibrium point , limit cycle , limit (mathematics) , differential equation , mathematical analysis , statistical physics , physics , acoustics
We study the dynamics of an autocatalator model, which is described by a 3‐dimensional autonomous cubic differential system. We analyze the number and local properties of equilibrium points of the system using methods of the qualitative theory of ordinary differential equations. We also investigate small‐amplitude limit cycles bifurcating from an equilibrium state of the system. Some numerical simulations illustrating the obtained theoretical results are presented.