Abstract
In this paper, we study a dynamic structure of discretized vector fields obtained from the Brusselator, which is described by two-dimensional ordinary differential equations (ODEs). We found that a bifurcation structure of the logistic map is embedded in the discretized vector field. The embedded bifurcation structure was unraveled by the dynamical orbits that eventually converge to a fixed point. We provide a detailed mathematical analysis to explain this phenomenon and relate it to the solution of the original ODEs.
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