Dynamics and bifurcations of two coupled neural oscillators with different connection types
| Autor: | Roman Borisyuk, Dirk Roose, Galina Borisyuk, Alexander I Khibnik |
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| Rok vydání: | 1995 |
| Předmět: |
Computer science
General Mathematics Models Neurological Immunology Chaotic Topology General Biochemistry Genetics and Molecular Biology Synchronization Control theory Oscillometry Animals Bifurcation Multistability General Environmental Science Neurons Pharmacology Network architecture Quantitative Biology::Neurons and Cognition Artificial neural network General Neuroscience Information processing Brain Computational Theory and Mathematics Quasiperiodic function Neural Networks Computer Nerve Net General Agricultural and Biological Sciences Mathematics |
| Zdroj: | Bulletin of Mathematical Biology. 57:809-840 |
| ISSN: | 1522-9602 0092-8240 |
| Popis: | In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory--excitatory, excitatory--inhibitory, inhibitory--excitatory, and inhibitory--inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodic in-phase oscillations, while the connection of populations of the same type lead to periodic anti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central ¿top level¿ subcortical circuit (e.g., the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus. |
| Databáze: | OpenAIRE |
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