Transcript
Parasitic Lives in the Atlantic Ocean,
Mediterranean Sea, and Great Lakes Up to 35.5 inches
Pure entrainment: Phase differences all tend to a constant.
We add a forcer and look for all the oscillators to be entrained with the forcer.
Example of entrainment
Spinal
Cord
Sinusoidal Forcing arm
Electrodes
Dr. Kathleen Hoffman Dr. Eric Tytell Dr. Avis Cohen Dr. Tim Kiemel
Entrainment
No Entrainment
1 2 3
ωf
+ a sin(Θ2 – Θ1 +
Ψa)
+ d sin(Θ2 – Θ3 + Ψd) + f sin(Θf – Θ2 + Ψf)
Toy Model
+ d sin(Θ1 – Θ2 + Ψd) + a sin(Θ3 – Θ2 + Ψa)
ωf
Θ1’ =
Θ2’ =
Θ3’ =
ω
Θf’ =
ω
ω
Nearest neighbor coupling, any oscillator can be forced
With nearest neighbor coupling
1 2
ωf
+ a sin(Θ2 – Θ1) + d sin(Θ1 – Θ2 ) + f sin(Θf – Θ2)
ωf
Θ1’ =
Θ2’ =
ω
Θf’ =
ω
We determine the Jacobian
And evaluate the determinant,
And the trace
Fixed Points No Fixed Points
With nearest neighbor coupling
1 2 3
ωf
With nearest neighbor coupling
1 2 3
ωf
Three oscillators with one end forced.
Three oscillators with forcing in the middle.
2 3 4
ωf
1 5 n…
Five oscillators with the head forced
Five oscillators with forcing in the middle.
Calibrate our analysis with Eric’s data Look at different coupling systems
Symmetry in the two oscillator system. Phase shifting Entrainment range limits
N-Oscillators with the head forced.
N-Oscillators with the tail forced.
Dr. Joseph Previte Dr. Michael Rutter UMBC Team
› Dr. Kathleen Hoffman› Dr. Eric Tytell› Dr. Avis Cohen› Dr. Tim Kiemel
National Science Foundation
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