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Literature DB >> 4078499

The behavior of rings of coupled oscillators.

Abstract

Coupled oscillators in a ring are studied using perturbation and numerical methods. Stability of waves with nearest neighbor weak coupling is shown for a class of simple oscillators. Linkens' model for colorectal activity is analyzed and several stable modes are found. Stability of waves with general (non nearest neighbor coupling) is determined and comparisons to the nearest neighbor case are made. Approximate solutions to a ring with inhomogeneities are compared with numerical simulations.

Mesh：

Year: 1985 PMID： 4078499 DOI： 10.1007/BF00276558

Source DB: PubMed Journal: J Math Biol ISSN： 0303-6812 Impact factor: 2.259

12 in total

1. Synchronization of non-linear biochemical oscillators coupled by diffusion.

Authors: V Torre
Journal: Biol Cybern Date: 1975 Impact factor: 2.086

2. Mathematical modeling of the colorectal myoelectrical activity in humans.

Authors: D A Linkens; I Taylor; H L Duthie
Journal: IEEE Trans Biomed Eng Date: 1976-03 Impact factor: 4.538

3. Frequency entrainment of coupled Hodgkin-Huxley-type oscillators for modeling gastro-intestinal electrical activity.

Authors: D A Linkens; S Datardina
Journal: IEEE Trans Biomed Eng Date: 1977-07 Impact factor: 4.538

4. Dynamics of pattern formation in lateral-inhibition type neural fields.

Authors: S Amari
Journal: Biol Cybern Date: 1977-08-03 Impact factor: 2.086

5. Simulation of the electric-control activity of the stomach by an array of relaxation oscillators.

Authors: S K Sarna; E E Daniel; Y J Kingma
Journal: Am J Dig Dis Date: 1972-04

6. Simulation of the electrical and mechanical gradient of the small intestine.

Authors: T S Nelsen; J C Becker
Journal: Am J Physiol Date: 1968-04

7. The stability of entrainment conditions for RLC coupled Van der Pol oscillators used as a model for intestinal electrical rhythms.

Authors: D A Linkens
Journal: Bull Math Biol Date: 1977 Impact factor: 1.758

8. Simulation of intrinsic bursting in CA3 hippocampal neurons.

Authors: R D Traub
Journal: Neuroscience Date: 1982-05 Impact factor: 3.590

9. Two coupled neural oscillators as a model of the circadian pacemaker.

Authors: M Kawato; R Suzuki
Journal: J Theor Biol Date: 1980-10-07 Impact factor: 2.691

10. Cellular mechanism of neuronal synchronization in epilepsy.

Authors: R D Traub; R K Wong
Journal: Science Date: 1982-05-14 Impact factor: 47.728

10 in total

1. Dynamics from a time series: can we extract the phase resetting curve from a time series?

Authors: S A Oprisan; V Thirumalai; C C Canavier
Journal: Biophys J Date: 2003-05 Impact factor: 4.033

2. Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience.

Authors: Peter Ashwin; Stephen Coombes; Rachel Nicks
Journal: J Math Neurosci Date: 2016-01-06 Impact factor: 1.300

3. Computation of the internal forces in cilia: application to ciliary motion, the effects of viscosity, and cilia interactions.

Authors: S Gueron; K Levit-Gurevich
Journal: Biophys J Date: 1998-04 Impact factor: 4.033

The behavior of rings of coupled oscillators.

1. Synchronization of non-linear biochemical oscillators coupled by diffusion.

2. Mathematical modeling of the colorectal myoelectrical activity in humans.

3. Frequency entrainment of coupled Hodgkin-Huxley-type oscillators for modeling gastro-intestinal electrical activity.

4. Dynamics of pattern formation in lateral-inhibition type neural fields.

5. Simulation of the electric-control activity of the stomach by an array of relaxation oscillators.

6. Simulation of the electrical and mechanical gradient of the small intestine.

7. The stability of entrainment conditions for RLC coupled Van der Pol oscillators used as a model for intestinal electrical rhythms.

8. Simulation of intrinsic bursting in CA3 hippocampal neurons.

9. Two coupled neural oscillators as a model of the circadian pacemaker.

10. Cellular mechanism of neuronal synchronization in epilepsy.

1. Dynamics from a time series: can we extract the phase resetting curve from a time series?

2. Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience.

3. Computation of the internal forces in cilia: application to ciliary motion, the effects of viscosity, and cilia interactions.

4. Cilia internal mechanism and metachronal coordination as the result of hydrodynamical coupling.

5. Robust phase-waves in chains of half-center oscillators.

6. Rapid synchronization through fast threshold modulation.

7. Anti-phase, asymmetric and aperiodic oscillations in excitable cells--I. Coupled bursters.

8. A group-theoretic approach to rings of coupled biological oscillators.

9. A computational role for bistability and traveling waves in motor cortex.

10. Multistability and anomalies in oscillator models of lossy power grids.