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Stability Analysis of Limit Cycles on Continuous-time Cyclic Connection Neural Networks

연속시간 모델 순환결합형 신경회로망에서의 리미트사이클의 안정성 해석

  • 박철영 (대구대학교 전자공학부)
  • Published : 2006.04.01

Abstract

An intuitive understanding of the dynamic pattern generation in asymmetric networks may be considered an essential component in developing models for the dynamic information processing. It has been reported that the neural network with cyclic connections generates multiple limit cycles. The dynamics of discrete time network with cyclic connections has been investigated intensively. However, the dynamics of a cyclic connection neural network in continuous-time has not been well-known due to the considerable complexity involved in its calculation. In this paper, the dynamic behavior of a continuous-time cyclic connection neural network, in which each neuron is connected only to its nearest neurons with binary synaptic weights of ${\pm}1$, has been investigated. Furthermore, the dynamics and stability of the network have been analyzed using a piece-wise linear approximation.

신경회로망을 동적 정보처리에 응용하기 위해서는 비대칭 결합 신경회로망에서 생성하는 동적 상태천이에 관한 직관적 이해가 필요하다. 자기결합을 갖고 결합하중치가 비대칭인 순환결합형 신경회로망은 복수 개의 리미트사이클을 기억할 수 있다는 것이 알려져 있다. 현재까지 이산시간 모델의 네트워크에 대한 상태천이 해석은 상세하게 이루어져 왔다. 그러나 연속시간모델에 대한 해석은 네트워크 규모의 증가에 따른 급격한 계산량의 증가 때문에 그다지 활발하게 연구가 이루어지지 않고 있다. 본 논문에서는 각 뉴런이 최근접 뉴런에만 이진화된 결합하중 +1 및 -1로 연결된 연속시간모델 순환결합형 신경회로망의 동적인 상태천이 특성을 해석하여 이산시간 모델에서 기억 가능한 리미트사이클과의 차이점을 분석하였다. 또한 뉴런의 활성화 함수가 완전선형인 경우와 구분선형 근사인 네트워크에 대한 리미트사이클의 안정성을 해석하였다.

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