  We present a new difference equation with two parameters c in [0,1] and A in
[1,4]. This equation is equivalent to the logistic mapping if c=1 and the
Morishita mapping if c=0, which are the well-known chaotic and integrable
mappings, respectively. We first consider the case A=4 and investigate the time
evolution by changing the parameter c in [0,1]. We next change both two
parameters A in [3,4] and c in [0,1] and present the corresponding 3D
bifurcation diagram.
