Bifurcation in a nonlinear steady state system

• Autorzy: Wang G. Q. , Cheng S. S.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

bifurcation; cellular neural network; steady state; Krasnoselsky fixed point theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2010
• Tom: Vol. 30, no. 3
• Strony: 349--360
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Wang G. Q.

autor

Cheng S. S.

• Guangdone Polytechnic Normal University Department of Computer Science Guangzhou, Guangdone 510665, P. R. China,

Bibliografia

• [1] G.Q. Wang, S.S. Cheng, Periodic solutions of a bang bang recurrence equation with least periods 1 through 8, J. Difference Equ. Appl., to appear.
• [2] G.Q. Wang, S.S. Cheng, Notes on periodic solutions of discrete steady state systems, Port. Math. 64 (2007) 1, 3–10.
• [3] G.Q. Wang, S.S. Cheng, Multiple steady state solutions of a circular neural network, Chaos Solitons Fractals 37 (2008) 4, 1228–1232.
• [4] G.Q. Wang, S.S. Cheng, Fixed point theorems arising from seeking steady states of neural networks, Applied Math. Model. 33 (2009) 1, 499–506.
• [5] G.Q. Wang, S.S. Cheng, Elementary variational approach to zero free solutions of a nonlinear eigenvalue problem, Nonlinear Anal. 69 (2008), 3030–3041.
• [6] G.Q. Wang, S.S. Cheng, Variational approach to positive and negative steady state solutions of a circular neural network, J. Difference Equ. Appl., to appear.