Complete Asymptotic Analysis Of A Nonlinear Difference Equation With Piecewise Constant Control

Difference equation is always used in studying dynamical system, we can research in a deep-going way algorithms and properties of neural network system by dynamics. Study of large-scale network is difficult, Since there are only limited materials on basic asymptotic behaviors of discrete time dynamical systems with piecewise smooth nonlinearities, so it is very useful to establish simple and practical mathematical methods. In this paper, one such equation is the following where a∈(0,1), b, c∈(0,+∞) and f is a filter nonlinear function hereλ> 0.Note that given initial value (x₂, x-1)∈R2, we may compute the numbers xo, x1, x2,... in a unique manner. we are able to obtain a complete asymptotic analysis.