Table A1. Summary of nonlinear behavior... | Rockefeller University Press

Table A1.

Summary of nonlinear behavior in variants of the recruitment component RD model

Model variant	A	B	C	D	E	F	G	H
Starting model: $\frac{d η (t)}{d t} = - b η (t) + β_{0} [l (t) - l_{0}]$	✓	—	—	—	—	—	—	—
Velocity-dependent recruitment: $\frac{d η (t)}{d t} = - b η (t) + β_{0} [l (t) - l_{0}] - γ \frac{d l}{d t}$	—	—	—	—	✓	—	—	—
Distortion-dependent recruitment: $\frac{d η (t)}{d t} = - b η (t) + β_{0} [l (t) - l_{0}] - γ f (x) η (t)$
$f (x) = \frac{x (t) - x_{0}}{x_{0}}$	✓	—	—	—	✓	—	—	—
$f (x) = a b s [\frac{x (t) - x_{0}}{x_{0}}]$	✓	✓	✓	—	—	—	—	✓
$f (x) = {[\frac{x (t) - x_{0}}{x_{0}}]}^{2}$	✓	✓	✓	✓	✓	—	✓	✓

Model variant	A	B	C	D	E	F	G	H
Starting model: $\frac{d η (t)}{d t} = - b η (t) + β_{0} [l (t) - l_{0}]$	✓	—	—	—	—	—	—	—
Velocity-dependent recruitment: $\frac{d η (t)}{d t} = - b η (t) + β_{0} [l (t) - l_{0}] - γ \frac{d l}{d t}$	—	—	—	—	✓	—	—	—
Distortion-dependent recruitment: $\frac{d η (t)}{d t} = - b η (t) + β_{0} [l (t) - l_{0}] - γ f (x) η (t)$
$f (x) = \frac{x (t) - x_{0}}{x_{0}}$	✓	—	—	—	✓	—	—	—
$f (x) = a b s [\frac{x (t) - x_{0}}{x_{0}}]$	✓	✓	✓	—	—	—	—	✓
$f (x) = {[\frac{x (t) - x_{0}}{x_{0}}]}^{2}$	✓	✓	✓	✓	✓	—	✓	✓

linear F₁ versus ΔL relationship and linear F_SS versus ΔL relationship; B, difference in shape between large-amplitude quick stretch (rapid fall to a well-defined nadir, followed by a slower rise to an eventual steady state) and large-amplitude quick release (monotonic rise to the eventual steady state); C, difference in pattern among various amplitude quick stretches (trajectories tend to converge at a common nadir) and various amplitude quick releases (trajectories remain apart and distinct); D, difference in shape between small-amplitude (rapid rise to a zenith, followed by a slower fall to eventual steady state) and large-amplitude (monotonic rise to the eventual steady state) quick releases; E, quasi–mirror image responses of small-amplitude quick stretch and quick release; F, curvilinear up in F₂₃ versus ΔL relationship; G, downward trend in T₂₃ versus ΔL relationship, indicating that approach to nadir in response to large ΔL is faster than approach to nadir in response to small ΔL; H, downward trend in T₉₀ versus ΔL relationship.

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