On embedded bifurcation structure in some discretized vector fields.
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.
Kang
Hunseok
H
Research Institute for Electronic Science, Hokkaido University, Kita-ku, Sapporo, Japan. kang@math.sci.hokudai.ac.jp
Tsuda
Ichiro
I
D000200:Action Potentials / Q000502:physiology*; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods; D009435:Synaptic Transmission / Q000502:physiology*