Singular perturbation analysis of competitive neural networks with different time scales
The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this pap...
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| Veröffentlicht in: | Neural computation Jg. 8; H. 8; S. 1731 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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15.11.1996
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| ISSN: | 0899-7667 |
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| Abstract | The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points. |
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| AbstractList | The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points. The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points.The dynamics of complex neural networks must include the aspects of long- and short-term memory. The behavior of the network is characterized by an equation of neural activity as a fast phenomenon and an equation of synaptic modification as a slow part of the neural system. The main idea of this paper is to apply a stability analysis method of fixed points of the combined activity and weight dynamics for a special class of competitive neural networks. We present a quadratic-type Lyapunov function for the flow of a competitive neural system with fast and slow dynamic variables as a global stability method and a modality of detecting the local stability behavior around individual equilibrium points. |
| Author | Meyer-Bäse, A Ohl, F Scheich, H |
| Author_xml | – sequence: 1 givenname: A surname: Meyer-Bäse fullname: Meyer-Bäse, A organization: Institute for Flight Mechanics and Control, Darmstadt, Germany – sequence: 2 givenname: F surname: Ohl fullname: Ohl, F – sequence: 3 givenname: H surname: Scheich fullname: Scheich, H |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/8888615$$D View this record in MEDLINE/PubMed |
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| Title | Singular perturbation analysis of competitive neural networks with different time scales |
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