Real fixed points and dynamics of one parameter family of function (bx-1)‎ x

Abstract EN

In this paper, the real fixed points and dynamics of one parameter family of functions fkðxÞ 1⁄4 kfðxÞ; k > 0, where fðxÞ1⁄4ðb x 1Þ = x; x-0 and fð0Þ 1⁄4 ln b for b > 0; b-1, are investi-gated.

The real fixed points of fkðxÞ as well as their nature are explored.

For 0 < b < 1, it is seen that one fixed point of fkðxÞ is attracting and one fixed point is repelling for 0 < k < k and fkðxÞ has no real fixed points for k > k.

It is also found that the bifurcation in the real dynamics offkðxÞ occurs at the real parameter value k.

For b > 1, similar results are shown.