Double boundary value problem (A. Bose and J.E. Rubin, 2015)

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Accession:185334
For two neurons coupled with mutual inhibition, we investigate the strategies that each neuron should utilize in order to maximize the number of spikes it can fire (or equivalently the amount of time it is active) before the other neuron takes over. We derive a one-dimensional map whose fixed points correspond to periodic anti-phase bursting solutions. The model here solves a novel double boundary value problem that can be used to obtain the graph of this map. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218127415400040
Reference:
1 . Bose A, Rubin JE (2015) Strategies to Maximize Burst Lengths in Rhythmic Anti-Phase Activity of Networks with Reciprocal Inhibition International Journal of Bifurcation and Chaos 25(07):1540004
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Abstract integrate-and-fire leaky neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP;
Model Concept(s): Oscillations;
Implementer(s): Rubin, Jonathan E [jonrubin at pitt.edu];
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BoseRubin2015
readme.txt
doublebvp.ode
                            
# doublebvp.ode
# used for Bose and Rubin, IJBC, Vol. 25, June 30, 2015

# integrate 4 trajectories simultaneously

# (v,g) is the suppressed cell on its last cycle before it becomes active
v'=P*(I-v-g*(v-E)) 
g'=P*(-beta*g)

# (vhat,ghat) is the active cell on its last cycle of being active; ghat \equiv 0
vhat'=P*(I-vhat)

# (vtilde,gtilde) is the formerly suppressed cell on the cycle after its first reset
vtilde'=Q*(I-vtilde-gtilde*(vtilde-E))
gtilde'=Q*(-beta*gtilde)

# (vstar,gstar) is the formerly active cell on the cycle after it is first inhibited
vstar'=Q*(I-vstar-gstar*(vstar-E))
gstar'=Q*(-beta*gstar)

# two trivial equations are added, so that number of eqns = number of BCs
P'=0
Q'=0

# BCs
b v-1
b v'-1
b g-g0
b vhat
b vtilde
b vtilde'-1
b g'-gtilde
b vhat'-vstar
b vstar'-1

init P=0.65,Q=1.02,v=1,g=1.1,vstar=.96,gstar=1.24
par beta=0.2,I=2,E=-0.1,g0=1.1
@ total=1,dt=.01
done

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