Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable

Norikazu Takahashi; Tetsuo Nishi

doi:10.1109/TCSII.2006.876466

Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable

Norikazu Takahashi, Tetsuo Nishi

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.

Original language	English
Pages (from-to)	727-733
Number of pages	7
Journal	IEEE Transactions on Circuits and Systems II: Express Briefs
Volume	53
Issue number	8
DOIs	https://doi.org/10.1109/TCSII.2006.876466
Publication status	Published - 2006
Externally published	Yes

Keywords

Cellular neural networks (CNNs)
complete stability
planar dynamical systems

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/TCSII.2006.876466

Cite this

@article{92312df363ec49108c706efada6377e1,

title = "Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable",

abstract = "We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.",

keywords = "Cellular neural networks (CNNs), complete stability, planar dynamical systems",

author = "Norikazu Takahashi and Tetsuo Nishi",

year = "2006",

doi = "10.1109/TCSII.2006.876466",

language = "English",

volume = "53",

pages = "727--733",

journal = "IEEE Transactions on Circuits and Systems II: Express Briefs",

issn = "1549-7747",

number = "8",

}

TY - JOUR

T1 - Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable

AU - Takahashi, Norikazu

AU - Nishi, Tetsuo

PY - 2006

Y1 - 2006

N2 - We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.

AB - We study global dynamical behavior of cellular neural networks (CNNs) consisting of two cells. Since the output characteristic of each cell is expressed by a piecewise-linear function, a CNN with two cells is considered as a planar piecewise-linear dynamical system. We present the necessary and sufficient condition for such a CNN to be completely stable under the assumptions that: 1) self-coupling coefficients take the same value greater than one and 2) biases are set to zero. The condition is explicitly expressed in terms of coupling coefficients between cells.

KW - Cellular neural networks (CNNs)

KW - complete stability

KW - planar dynamical systems

UR - http://www.scopus.com/inward/record.url?scp=33748523045&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33748523045&partnerID=8YFLogxK

U2 - 10.1109/TCSII.2006.876466

DO - 10.1109/TCSII.2006.876466

M3 - Article

AN - SCOPUS:33748523045

SN - 1549-7747

VL - 53

SP - 727

EP - 733

JO - IEEE Transactions on Circuits and Systems II: Express Briefs

JF - IEEE Transactions on Circuits and Systems II: Express Briefs

IS - 8

ER -

Necessary and Sufficient Condition for a Class of Planar Dynamical Systems Related to CNNs to be Completely Stable

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this