Bifurcation in a nonlinear steady state system
Gen-Qiang Wang, Sui Sun Cheng · Opuscula Mathematica · 2010
The steady state solutions of a nonlinear digital cellular neural network with ω neural units and a nonnegative variable parameter λ are sought.We show that λ = 1 is a critical value such that the qualitative behavior of our network changes.More specifically, when ω is odd, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ ∈ [1, ∞), steady states cannot exist; while when ω is even, then for λ ∈ [0, 1), there is one positive and one negative steady state, and for λ = 1, there are no nontrivial steady states, and for λ ∈ (1, ∞), 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.