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Complete set of periodic solutions of a discontinuous recurrence equation
Authors:Yen Chih Chang  Gen-qiang Wang
Affiliation:1. Library, Tsing Hua University , Hsinchu , 30043 , Taiwan ROC;2. Department of Computer Science , Guangdong Polytechnic Normal University , Guangzhou , Guangdong , 510663 , P.R. China
Abstract:A nonlinear three-term recurrence relation arising from seeking the steady states of a cellular neural network with bang‐bang control is studied. We show that each solution is periodic and its prime period can be determined by three of its consecutive terms. By means of this periodicity property, we may then solve the steady state problem which to our knowledge is not solved by other means.
Keywords:nonlinear recurrence relation  heaviside function  neural network  steady state  periodic sequence  prime period
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