The called doping superlattice is that n-type and p-type impurity are doped alternately on a substrate material

thus forming 1-dimension periodic structure with n-i-p-i-n-i-p-i…arrange.The conductor band botton of the substrate material is modulated periodically by alternately dopping

leading to shape similar to sine-squared potential.The particle motion equation is reduced to the general pendulum equation with a dampping and a force terms in the classical mechanics frame based on the bistable state effect of the superlattice quantum well. The equations solution and the period of a particle motion are found strictlly by Jacobian ellipse function and the 1st kind ellipse integral for the non-perturbed system.The global bifurcation and a chaotic behaours with the Smale horseshoe were analysed by Melnikov method.The critical condition through to a chaos based on a cascade bifurcation was found. It shown that the chaotic oscillation with the Smale horseshoe exits in the system for the separatrive orbit; odd-order subharmoric bifurcations found also for the oscillation periodic orbit.Noting to critical condition entered in a chaos being related to the parameters of the system

the chaos can be avoided or controlled.The theoretical analyse is provided to the design of the optical bistable state cell.