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Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.

Massarelli N, Clapp G, Hoffman K, Kiemel T - J Math Neurosci (2016)

Bottom Line: This results in a simpler model yet maintains some properties of the neural model.Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results.In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA.

ABSTRACT
Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bending stimulus, that is, in the presence of a rhythmic signal, the CPG will change its frequency to match the stimulus frequency. Bending experiments in which the lamprey spinal cord has been removed and mechanically bent back and forth at a single point have been used to determine the range of frequencies that can entrain the CPG rhythm. First, we model the lamprey locomotor CPG as a chain of neural oscillators with three classes of neurons and sinusoidal forcing representing edge cell input. We derive a phase model using the connections described in the neural model. This results in a simpler model yet maintains some properties of the neural model. For both the neural model and the derived phase model, entrainment ranges are computed for forcing at different points along the chain while varying both intersegmental coupling strength and the coupling strength between the forcer and chain. Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results. In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model. Both biological experiments and the robustness of non-monotonic entrainment ranges as a function of the forcing position across different classes of CPG models with nonuniform asymmetric coupling suggest that a specific property of the intersegmental coupling of the CPG is key to entrainment.

No MeSH data available.


Related in: MedlinePlus

Example of loss of entrainment for the derived phase model. The coupling parameters are the same as those shown in Fig. 10. We see that entrainment is lost in the same way for both the neural and the derived phase model, further supporting that the phase model contains the same entrainment information
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Fig11: Example of loss of entrainment for the derived phase model. The coupling parameters are the same as those shown in Fig. 10. We see that entrainment is lost in the same way for both the neural and the derived phase model, further supporting that the phase model contains the same entrainment information

Mentions: Entrainment ranges for the neural and derived phase models as a function of the forcing strength. Leftpanel illustrates entrainment ranges as a function of the forcing strength for weak intersegmental coupling corresponding to , , and . Rightpanel illustrates entrainment ranges for 100 times stronger intersegmental coupling with and . Note that for weak coupling the entrainment ranges for the neural and derived phase models match closely while for strong coupling the entrainment ranges start to differ as the forcing strength increases. Thedashedline on both plots represents Hopf bifurcations that occur when entrainment is lost. Smoothlines denote saddle-node bifurcations. Thearrows in right panel correspond to the forcing strength values where loss of entrainment is depicted in Figs. 10 and 11


Entrainment Ranges for Chains of Forced Neural and Phase Oscillators.

Massarelli N, Clapp G, Hoffman K, Kiemel T - J Math Neurosci (2016)

Example of loss of entrainment for the derived phase model. The coupling parameters are the same as those shown in Fig. 10. We see that entrainment is lost in the same way for both the neural and the derived phase model, further supporting that the phase model contains the same entrainment information
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4835419&req=5

Fig11: Example of loss of entrainment for the derived phase model. The coupling parameters are the same as those shown in Fig. 10. We see that entrainment is lost in the same way for both the neural and the derived phase model, further supporting that the phase model contains the same entrainment information
Mentions: Entrainment ranges for the neural and derived phase models as a function of the forcing strength. Leftpanel illustrates entrainment ranges as a function of the forcing strength for weak intersegmental coupling corresponding to , , and . Rightpanel illustrates entrainment ranges for 100 times stronger intersegmental coupling with and . Note that for weak coupling the entrainment ranges for the neural and derived phase models match closely while for strong coupling the entrainment ranges start to differ as the forcing strength increases. Thedashedline on both plots represents Hopf bifurcations that occur when entrainment is lost. Smoothlines denote saddle-node bifurcations. Thearrows in right panel correspond to the forcing strength values where loss of entrainment is depicted in Figs. 10 and 11

Bottom Line: This results in a simpler model yet maintains some properties of the neural model.Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results.In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics and Statistics, University of Maryland, Baltimore County, 1000 Hilltop Circle, Baltimore, MD, 21250, USA.

ABSTRACT
Sensory input to the lamprey central pattern generator (CPG) for locomotion is known to have a significant role in modulating lamprey swimming. Lamprey CPGs are known to have the ability to entrain to a bending stimulus, that is, in the presence of a rhythmic signal, the CPG will change its frequency to match the stimulus frequency. Bending experiments in which the lamprey spinal cord has been removed and mechanically bent back and forth at a single point have been used to determine the range of frequencies that can entrain the CPG rhythm. First, we model the lamprey locomotor CPG as a chain of neural oscillators with three classes of neurons and sinusoidal forcing representing edge cell input. We derive a phase model using the connections described in the neural model. This results in a simpler model yet maintains some properties of the neural model. For both the neural model and the derived phase model, entrainment ranges are computed for forcing at different points along the chain while varying both intersegmental coupling strength and the coupling strength between the forcer and chain. Entrainment ranges for chains with nonuniform intersegmental coupling asymmetry are larger when forcing is applied to the middle of the chain than when it is applied to either end, a result that is qualitatively similar to the experimental results. In the limit of weak coupling in the chain, the entrainment results of the neural model approach the entrainment results for the derived phase model. Both biological experiments and the robustness of non-monotonic entrainment ranges as a function of the forcing position across different classes of CPG models with nonuniform asymmetric coupling suggest that a specific property of the intersegmental coupling of the CPG is key to entrainment.

No MeSH data available.


Related in: MedlinePlus