Chaos in ionic transport through membranes

The chaotic nature of ionic current through nuclear filters has been detected and analyzed by means of Liapunov exponents and bifurcation diagrams. The "crowd model" describing the nonlinear behavior of single channel ionic current, based on the family of logistic maps, has been formulated and applied to analysis of the patch clamp recordings. Some characteristic features of the system read out from the bifurcation diagrams of the two-parameter logistic map, and also from the extended Hodgkin-Huxley theory have been presented. The relation between the logistic difference schemes (and, at the same time, the class of logistic differential equations) and the logistic maps as well as some possibilities of using the crowd model to biological membranes have also been shown.