The　formation　mechanism　of　network　traffic　flow　and　its　evolution　law　are　closely　related　to　daily　activities　of　travelers.　The　current　studies　indicate　that　the　law　of　network　traffic　flow　evolution　is　day-to-day;　therefore,　using　days　as　the　scale　unit　is　an　important　way　to　illustrate　the　evolution　of　network　traffic　flow.　In　previous　studies,　travelers　in　the　network　were　tacitly　assumed　to　be　entirely　rational.　When　the　rationality　of　travelers　is　limited,　the　dynamics　of　the　evolution　law　needs　to　be　re-examined.　This　paper　presents　the　utility　maximization　hypothesis　in　a　logit　model　by　using　the　＂bounded　rationality＂　hypothesis　and　develops　a　bounded　rational　binary　logit　(BRBL)　model.　We　apply　the　BRBL　model　to　a　day-to-day　network　traffic　flow　distribution　and　discuss　the　evolution　law　of　day-to-day　network　traffic　flow　under　the　assumption　of　the　limited　rationality　of　travelers.　Through　a　numerical　experiment,　this　paper　analyzes　the　evolution　characteristics　of　network　traffic　flow.　The　results　are　as　follows.　Firstly,　the　final　state　of　the　network　traffic　flow　process　is　not　only　correlated　to　the　cost-sensitivity　of　travelers　and　dependence　on　actual　cost,　but　also　strongly　related　to　the　degree　of　the　nationality　of　travelers.　Secondly,　the　system　will　be　either　bifurcated　or　chaotic　when　either　cost-sensitivity　increases　or　dependence　on　actual　cost　increases.　Moreover,　within　the　group　of　travelers　whose　rationality　level　is　low,　no　matter　what　the　cost-sensitivity　of　travelers　and　the　dependence　on　actual　cost　are,　the　evolution　results　are　asymptotically　stable.　Finally,　in　particular,　in　certain　circumstances,　it　is　easy　to　achieve　stability　when　the　rationallty　degree　of　travelers　is　very　high　or　very　low,　while　it　is　not　easy　to　achieve　stability　when　the　rationality　degree　of　travelers　is　medium.