Analysis of Flux‐Ratio Bifurcation in Ionic Flows via Classical Poisson–Nernst–Planck Models

ABSTRACT The flux ratio serves as a valuable characteristic for assessing the influence of permanent charge on the fluxes of different ion species. Our work analyzes flux ratios and their bifurcations in ionic flows using Poisson–Nernst–Planck models. Unlike Ussing's and Hodgkin–Keynes's ratios, our flux‐bifurcation analysis captures the emergence and disappearance of multiple flux‐ratio solutions as boundary conditions and permanent charge vary. We identify bifurcation points for flux ratios and characterize their dependence on system parameters, such as boundary conditions and permanent charge. Specifically, we examine the qualitative behavior of fluxes and flux ratios with respect to current, boundary concentrations, and boundary electric potentials at bifurcation points. This study can contribute to a deeper understanding of the underlying mechanisms governing ionic flows and could offer valuable insights for the design and optimization of ion channels in practical applications.