Abstract
The paper deals with dynamical behaviors of the solutions of a single neuronic equation: x(t+1) = 1[ ∑ k=0 n−1 akx(t−k)θ] , where 1[ u] = 1 for u>0 and = 0 for u≦0, in order to have a systematic insight into a certain family of transition phenomena among 2 n state configurations. For this purpose we are concerned with the specific operators of the six kinds: L ω, L ̄omega;, L α l , L ̄alpha; l , L β l and L ̄beta; l ( l=0, 1, 2,…, n−1). In Sections 5 and 6 we discuss reverberation phenomena for L ̄alpha; 0. A regular articular representation of each state configuration is used to find out all the types and the total number of reverberation cycles under the applications of the operator L ̄alpha; 0. Section 7 deals with the applications of L ālpha; n−1 , while Sections 8 and 9 deal with L ̄beta; l . Section 10 gives some ideas on the use of our family of operators for the representation of the linear threshold functions associated with the single neuronic equation.
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