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\iteman{io-port 06016594}
\itemau{Wang, Gen-Qiang; Cheng, Sui Sun}
\itemti{Periodic solutions of a bang bang recurrence equation with least periods 1 through 8.}
\itemso{J. Difference Equ. Appl. 18, No. 2, 195-221 (2012).}
\itemab
Summary: We study a very simple three term recurrence relation involving the discontinuous Heaviside step function. One reason for studying such an relation is that solutions of our recurrence relation are steady state distributions in some basic neural network models. Since analytic tools cannot be used to handle discontinuous models such as ours, existence of periodic solutions is investigated by combining combinatorial elimination technique as well as existence arguments for linear systems. By such means, we are able to obtain all periodic solutions with least periods 1 through 8. Some periodic solutions with periods 12, 20 and 36 can also be found, but exhaustive results are not yet available.
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\itemut{bang-bang recurrence relation; periodic solution; neural network; discontinuous control}
\itemli{doi:10.1080/10236190902841984}
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