Table 1.

Key Notation

Term	Description
d	constant supraspinal drive fed to CPG neurons
q	limb angle with the horizontal
v	limb angular velocity
Ia-F, II - F	feedback terms to the flexor side
Ia - E, Ib - E	feedback terms to the extensor side
FBk	total summed feedback to neuron k
FBcrit	feedback required to excite an inactive In above threshold; independent of drive
TTC	Stance Transition Curve; location in limb phase space where flexor activates
WTC	Swing Transition Curve; location in limb phase space where extensor activates
eStance	portion of the locomotor phase where Mn - E is active and ground reaction is present
fStance	portion of the locomotor phase where Mn - F is active and ground reaction is present
eSwing	portion of the locomotor phase where Mn - E is active and ground reaction is absent
fSwing	portion of the locomotor phase where Mn - F is active and ground reaction is absent
I	moment of inertia of limb with respect to suspension point
K	coefficient of gravitational moment
b	angular viscosity in the hinge joint
MGRmax	amplitude of moment of ground reaction force
ME, MF, MGR	moment applied to limb from flexor, extensor, or ground reaction
f	function that calculates the output activity of each neuron
H	heaviside function that calculates inhibitory output in the reduced model
mphase	fixed, drive-dependent motoneuron output during phase; obtained from time average of original model
{}	notation indicating that the constant within is piecewise (phasewise) defined
xε; = (qε, vε)	saddle point of system ẋ = f(x) + ε;g(x) for ε ∈ [0, 1]
Wu(xε), Ws(xε)	unstable, stable manifold from xε
W̃s(xε)	trajectory governed by the eSwing vector field that converges to xε as v ↑ 0
γ0	homoclinic orbit emanating from x0
Σ	transversal to the flow
	Melnikov function; sign indicates how the homoclinic perturbs with increasing ε
$M_{\mathit{phase}}^{\ast }$	fixed muscle moment during phase; obtained to produce negative Melnikov sign
$h^k(\epsilon )=(h_q^k(\epsilon ),h_v^k(\epsilon ))$	intersection of the stable and unstable manifolds with Σ; k ∈ {u, s}