Phase portraits and bifurcation diagram of the Gray-Scott model

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.

Automated summary

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.