4.5.4 A Ring CPG Model with Negative Feedback
Kleinfeld and Sompolinsky also suggested ring oscillators as pattern generators. As in the case of the RI pair, a ring oscillator with positive feedback (all excitatory synapses around the ring) will be unstable. The net frequency around the ring rises to a saturation value set by the refractory periods of the neurons; no stable pattern is seen. If the ring uses negative feedback, as shown in Figure 4.5-10, and the epsp time constants, RPFM time constants, and pulse weights are "tuned," a stable, patterned burst oscillation around the ring will occur.
Four neurons are connected in a ring. N1 excites N2, N2 excites N3, N3 excites N4, and N4 inhibits N1, which is also excited with dc. The ring uses negative feedback and acts as a stable oscillator. The Simnon model for this candidate CPG is given below:
continuous system RINGOSC1 " 3/16/99
" Model for a neural ring of 4 oscillator using NFB.
STATE v1 v2 v3 v4 pi p2 p3 p4 q1 q2 q3 q4
DER dv1 dv2 dv3 dv4 dp1 dp2 dp3 dp4 dq1 dq2 dq3 dq4
dv1 = -c1*v1 + c1*E1 - z 1 " Neuron 1. RPFM model. w1 = IF v1 > phi1 THEN 1 ELSE 0 s 1 = DELAY (w1, tau) x1 = w1 - s1
y1 = IF x1 > 0 THEN x1 ELSE 0 z1 = y1*phi1/tau u1 = y1*Do1/tau dv2 = -c2*v2 + c2*E2 - z2 " Neuron 2. RPFM model.
w2 = IF v2 > phi 2 THEN 1 ELSE 0 s2 = DELAY (w2, tau) x2 = w2 - s2
y2 = IF x2 > 0 THEN x2 ELSE 0 z2 = y2*phi2/tau u2 = y2*Do2/tau dv3 = -c3*v3 + c3*E3 - z3 " N3 RPFM model.
w3 = IF v3 > phi 3 THEN 1 ELSE 0 s3 = DELAY (w3, tau) x3 = w3 - s3
y3 = IF x3 > 0 THEN x3 ELSE 0 z3 = y3*phi3/tau u3 = y3*Do3/tau dv4 = -c4*v4 + c4*E4 - z4 " N4 RPFM model inhibits N1. w4 = IF v4 > phi 4 THEN 1 ELSE 0 s4 = DELAY (w4, tau) x4 = w4 - s4
y4 = IF x4 > 0 THEN x4 ELSE 0 z4 = y4*phi4/tau u4 = y4*Do4/tau
" 2 TIME CONSTANT SYNAPSES:
dp4 = -a4*p4 + u4 " Inhibitory synapse dq4 = -b4*q4 + p4*a4*b4
" NEURON INPUTS:
E1 = Vin - q4" N1 has a dc clock drive input, Vin E2 = q1 E3 = q2 E4 = q3
" PLOTTING VARIABLES:
Was this article helpful?
This guide will help millions of people understand this condition so that they can take control of their lives and make informed decisions. The ebook covers information on a vast number of different types of neuropathy. In addition, it will be a useful resource for their families, caregivers, and health care providers.