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BIFURCATION ANALYSIS FOR A NONLINEAR RECURRENCE RELATION WITH THRESHOLD CONTROL AND PERIODIC COEFFICIENTS

CHENGMIN HOU

Department of Mathematics, Yanbian University, Yanji 133002, P. R. China

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CHUNLAI WANG

Department of Mathematics, Yanbian University, Yanji 133002, P. R. China

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SUI SUN CHENG

Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R. O. C.

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https://doi.org/10.1142/S0218127412500551Cited by:1 (Source: Crossref)

Abstract

A nonlinear recurrence involving a piecewise constant McCulloch–Pitts function and two 2-periodic coefficient sequences is investigated. By allowing the threshold parameter to vary from 0⁺ to +∞, we work out a complete bifurcation analysis for the asymptotic behaviors of the corresponding solutions. We show that there are four steady state solutions and that all solutions will tend to one of them. We hope that our results will be useful in further investigating neural networks involving the McCulloch–Pitts function with threshold and more general periodic coefficients.

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