The Asymptotic Analysis Of Anonlinear Difference Equation With Piecewise Constanat Control And Periodic Coeffient

Research of artificial neural networks has a very important role in various fields of automatic control, image processing, pattern recognition. It is a very meaningful work that use the theory of dynamics to research neural network algorithm and nature.Difference equation is mathematical model to study the the system of dynamics, so it is the commonly model to study the behavior of neural network dynamical.Since the massive network research is still lack of effective methods and tools, so the establishment of the small size, simple and practical mathematical model is becoming more and more important. This paper considers the following forms of where{an}n=0∞,{bn}n=0∞are2-period sequence,a0,a1∈(0,1),b0,bi,c0,c1,∈(0,+∞) when(x2n,x2n+1)=(yn,zn),The difference equation is equivalent to the following form of two dimensional dynamics system. and a0, a1∈(0,1),b0,b1,c0,c1∈(0,+∞),f is a filter nonlinear function, here λ>0. note that the given initial value (y-1,z-1)∈R+2, we may compute the numbers y0,z0, y1,z1…, So we may use the two dimensional autonomous dynamical system to deduce the asymptotic properties of difference equation.