TY  - JOUR
ID  - Wang2010
LB  - Wang2010
AU  - Wang, Gen-Qiang
AU  - Cheng, Sui Sun
TI  - Bifurcation in a nonlinear steady state system
ST  - Bifurcation in a nonlinear steady state system
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 3
SP  - 349
EP  - 360
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.3.349
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.3.349
AB  - The steady state solutions of a nonlinear digital cellular neural network with \(\omega\) neural units and a nonnegative variable parameter \(\lambda\) are sought. We show that \(\lambda = 1\) is a critical value such that the qualitative behavior of our network changes. More specifically, when \(\omega\) is odd, then for \(\lambda \in [0,1)\), there is one positive and one negative steady state, and for \(\lambda \in [1,\infty)\), steady states cannot exist; while when \(\omega\) is even, then for \(\lambda \in [0,1)\), there is one positive and one negative steady state, and for \(\lambda = 1\), there are no nontrivial steady states, and for \(\lambda \in (1,\infty)\), there are two fully oscillatory steady states. Furthermore, the number of existing nontrivial solutions cannot be improved. It is hoped that our results are of interest to digital neural network designers.
KW  - bifurcation
KW  - cellular neural network
KW  - steady state
KW  - Krasnoselsky fixed point theorem
SN  - 1232-9274
ER  -