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| The Dislocation Model of Superlattice and Dynamic Stabilities for system |
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Abstract The dynamic behaviours in the vicinity of the interface for the superlattice is discussed in the classical mechanics frame and based on Seeger equation.It is indicated that the motion and the accomulation of the dislocations by the bifurcation and chaos may be gived rise to the layer or the fracture of the superlattice;and also it is indicated that putting the superlattice of growing process in the suitable sound field reduce stress to minimum, or suitable regulating a parameters of the system, then the dynamic stabilities of the system may be ensured.At first,introducing damping term,the Seeger equation described the general dislocation motion may be reduced to the generalized pendulum equation described superlattice system.The properties of the phase plane for a non-peturbated system are ananysed by means of Jacobian elliptic function and the elliptic integral, and the solution of the equation and a period of the dislocation motion for this system may be expressed exactly。Secondary, the global bifurcation and a chaotic behaviours with the Smale horseshoe for the 3-kind orbit in a phase plane are analysed by Melnikov method.The critical condition of the system entered in a bifurcation or a chaoc is found。It show that the critical condition is related to the parameters of the system, then suitable regulating a parameters of the system,the bifurcation or the chaos can be avoided or controlled in principle，then the stabilities of the growing process and the perfect of the superlattice materials may be further ensured
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Received: 08 June 2010
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2011, Vol. 32 
