Project/Area Number  05452211 
Research Category 
GrantinAid for Scientific Research (B).

Research Field 
System engineering

Research Institution  KYUSHU UNIVERSITY 
Principal Investigator 
NISHI Tetsuo KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,PROFESSOR, 工学部, 教授 (40037908)

CoInvestigator(Kenkyūbuntansha) 
OOHAMA Yasusada KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,RESEARCH ASSOCIATE, 工学部, 助手 (20243892)
KAWANE Yuji KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,RESEARCH ASSOCIATE, 工学部, 助手 (30214662)
栖原 淑郎 九州大学, 工学部, 助手 (80187799)
KOHDA Tohru KYUSHU UNIVERSITY,FACULTY OF ENGINEERING,PROFESSOR, 工学部, 教授 (20038102)
KOGA Tosiro KURUME INSTITUTE OF TECHNOLOGY,PROFESSOR, 知能工学研究所, 教授 (00037706)

Project Fiscal Year 
1993 – 1994

Project Status 
Completed(Fiscal Year 1994)

Budget Amount *help 
¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1994 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1993 : ¥1,500,000 (Direct Cost : ¥1,500,000)

Keywords  Associative Memory / Neural Network / Storage Capacity / Recursive Neural Network / Stable Equilibrium / Limit Cycle / 連想記憶 / ニューラルネットワーク / 記憶容量 / 相互結合回路網 / 安定平衡点 / リミットサイクル 
Research Abstract 
The results obtained in the research term (19931994) are as follows : 1. We consider a neural network in which n neurons are arranged on a ring. We assume that each neuron is connected only with the preceding k (*n1) neurons and the coefficients of connections are tapered, that is, the magnitude of coefficients decrease along with distance. This model is derived from the real biological knowledge and is a special kind of CNNs (Cellular Neural Network). We examined the number of equilibrium points of the above neural networks and proved that (1) the number is only one for k=1 or 2, three for k=3, and four for k=4. 2. We may conjecture that the number of equilibrium points are extremely few for tapered neural networks. We therefore examined another limiting case where k=n1 and the magnitude of each coefficients is unity. We showed in this case that (1) there exist a network which can possess are at least 2^n/2 equilibrium points, and (2) there exists a network which can possess at least 2^n/4 stable equilibrium points. Thus we showed that the number of equilibrium points increases exponentially with k. 3. Concerning the stability of the CNN,we generalized the theorem recently given by Gilli. Gilli's theorem requires for a prescribed matrix A the condition that there exists a positive diagonal matrix D such that DA+A^TD is a symmetric matrix, while our theorem requires that GAMMA A+A^T GAMMA is a symmetric matrix where GAMMA is a positive definite matrix. 4. We gave the necessary and sufficient condition for a set of equilibrium points to be realizable by means of a neural network whose all diagonal elements have identical value and all nondiagonal elements are also identical. 5. In general equilibrium points correspond to solutions of a nonlinear resistive circuits. So we investigated about the number of solutions of these circuits and had many presentations as shown in REFERENCES below.
