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Literature DB >> 7459399

Coupled Van der Pol oscillators---a model of excitatory and inhibitory neural interactions.

Abstract

A system of mutually coupled Van der Pol equations is derived from an extended version of the Wilson and Cowan model for the dynamics of a number of excitatory and inhibitory neural subsets. In the lowest order of approximation, interactions between excitatory and inhibitory subsets appear as linear elastic coupling, while those within and between excitatory and excitatory subsets appear as nonlinear frictional coupling. The case of two coupled oscillators is investigated by the method of averaging and the stability conditions for two mode oscillations are obtained. Internal resonance is also discussed briefly in the case of identical oscillators.

Entities: Disease

Mesh：

Year: 1980 PMID： 7459399 DOI： 10.1007/bf00336943

Source DB: PubMed Journal: Biol Cybern ISSN： 0340-1200 Impact factor: 2.086

8 in total

1. Models of neuronal populations: the basic mechanisms of rhythmicity.

Authors: F H Lopes da Silva; A van Rotterdam; P Barts; E van Heusden; W Burr
Journal: Prog Brain Res Date: 1976 Impact factor: 2.453

Review 2. Linear analysis of the dynamics of neural masses.

Authors: W J Freeman
Journal: Annu Rev Biophys Bioeng Date: 1972

3. Excitatory and inhibitory interactions in localized populations of model neurons.

Authors: H R Wilson; J D Cowan
Journal: Biophys J Date: 1972-01 Impact factor: 4.033

4. Model of brain rhythmic activity. The alpha-rhythm of the thalamus.

Authors: F H Lopes da Silva; A Hoeks; H Smits; L H Zetterberg
Journal: Kybernetik Date: 1974-05-31

5. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue.

Authors: H R Wilson; J D Cowan
Journal: Kybernetik Date: 1973-09

6. Performance of a model for a local neuron population.

Authors: L H Zetterberg; L Kristiansson; K Mossberg
Journal: Biol Cybern Date: 1978-11-10 Impact factor: 2.086

7. Biological rhythms and the behavior of populations of coupled oscillators.

Authors: A T Winfree
Journal: J Theor Biol Date: 1967-07 Impact factor: 2.691

8. Nonlinear oscillations and electroencephalography.

Authors: E M Dewan
Journal: J Theor Biol Date: 1964-07 Impact factor: 2.691

8 in total

14 in total

1. A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG.

Authors: J D Victor; A Canel
Journal: Ann Biomed Eng Date: 1992 Impact factor: 3.934

2. Two-neurons network. I. Integrate and fire pacemaker models.

Authors: R Budelli; J Torres; E Catsigeras; H Enrich
Journal: Biol Cybern Date: 1991 Impact factor: 2.086

3. Autoregression models of EEG. Results compared with expectations for a multilinear near-equilibrium biophysical process.

Authors: J J Wright; R R Kydd; A A Sergejew
Journal: Biol Cybern Date: 1990 Impact factor: 2.086

Coupled Van der Pol oscillators---a model of excitatory and inhibitory neural interactions.

1. Models of neuronal populations: the basic mechanisms of rhythmicity.

Review 2. Linear analysis of the dynamics of neural masses.

3. Excitatory and inhibitory interactions in localized populations of model neurons.

4. Model of brain rhythmic activity. The alpha-rhythm of the thalamus.

5. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue.

6. Performance of a model for a local neuron population.

7. Biological rhythms and the behavior of populations of coupled oscillators.

8. Nonlinear oscillations and electroencephalography.

1. A relation between the Akaike criterion and reliability of parameter estimates, with application to nonlinear autoregressive modelling of ictal EEG.

2. Two-neurons network. I. Integrate and fire pacemaker models.

3. Autoregression models of EEG. Results compared with expectations for a multilinear near-equilibrium biophysical process.

4. A quantitative population model of whisker barrels: re-examining the Wilson-Cowan equations.

5. Nonlinear autoregressive analysis of the 3/s ictal electroencephalogram: implications for underlying dynamics.

6. A reinvestigation of the Geman-Miller respiratory oscillator model.

7. Model of bidirectional interaction between myocardial pacemakers based on the phase response curve.

8. Linear model of brain electrical activity--EEG as a superposition of damped oscillatory modes.

9. State-changes in the brain viewed as linear steady-states and non-linear transitions between steady-states.

10. A linear theory for global electrocortical activity and its control by the lateral hypothalamus.