Ice is quite literally correct.
No, not in the brain are there parallel excitation sources for the heart, unless you want to say the many neural cells sending signals to the vagus nerve are independent parallel systems OR that the vagus nerve, which has many individual nerve fibers (axons) carring their excitation down to the heart is as many systems as there are axons in the vagus nerve. You did make this second silly claim that parallel axons of a nerve bundle, should be considered parallel systems.
There are a large number of parallel functional pathways to ensure heartbeat. For example, dozens of nerve fibers in the vagus nerve provide downregulation to the heart...
It is ONE vagus nerve we consider as the path way not its few hundred axons for individual cells that are parallel systems. As you take that POV that every one of the cells driving signal down those axon is a separate parallel system too, then the brains does have sever hundred parallel system stimulating the heart, but why stop there - each of those cells driving action potential down an axon was in turn part of a neural oscillator network with more than a million cells - I.e. Why not claim there are at least a million distinguishable cells that work in parallel to stimulate the heart? - Answer: because that is a silly reductive POV. The heart is normally stimulated to beat by the (one) vagus nerve. We distinguish nerves from the axons that make them up. E.g. each eye has ONE optic nerve system.
Once we consider the Atrio Ventrial part of the heart, AV then yes there are two independent and physically separate parts of the AV that can drive, stimulate via His conduction fibers, the lower parts of the heart. That is where a mesh like electrode of heart pacer is attached. Although I know a lot about all this as helped develop the first good reliable pacemaker, which APL/JHU then licenses to MedTronics (and they made millions form it) I did follow your suggestion (as I have forgotten a lot in ~30 years since leaving that project.) But first let me clarify a point that is often is not mentioned: the AV node is a "triggerable one-shot oscillator" - normally one cycle produced for each brief and weak stimulation from the brain. I. e. the output of the AV node is much stronger and longer lasting than the pulse that triggered it. Its output goes down the fast conduction bundle of His to cause the lower ventral parts of the heart to contract.
Here, from first Google hit (Wiki) are some of the first facts stated, which illustrate my point well - namely two parallel systems for making heart contract don't normally exist as when they do they can cause problems even death:
http://en.wikipedia.org/wiki/AV_nodal_reentrant_tachycardia said:
... atrioventricular nodal reentrant tachycardia, AVNRT, is a type of tachycardia (fast rhythm) of the heart. It is a type of supraventricular tachycardia (SVT), meaning that it originates from a location within the heart above the bundle of His. AV nodal reentrant tachycardia is the most common regular supraventricular tachycardia. ... The main symptom is palpitations.
AVNRT occurs when a reentry circuit forms within or just next to the atrioventricular node. The circuit usually involves two anatomical pathways: the fast pathway and the slow pathway, which are both in the right atrium. The slow pathway, which is usually targeted for ablation, a treatment for AVNRT) is located inferior and slightly posterior to the AV node, often following the anterior margin of the coronary sinus. The fast pathway is usually located just superior and posterior to the AV node. These pathways are formed from tissue that behaves very much like the AV node, and some authors regard them as part of the AV node.
In common AVNRT, the anterograde conduction is via the slow pathway and the retrograde conduction is via the fast pathway ("slow-fast" AVNRT).
Because the retrograde conduction is via the fast pathway, stimulation of the atria (which produces the inverted P wave) will occur at the same time as stimulation of the ventricles (which causes the QRS complex). As a result, the inverted P waves may not be seen on the surface ECG since they are buried with the QRS complexes. ...
Let me amplify this:
"The slow pathway, which is usually targeted for ablation, (a treatment for AVNRT) is located inferior and slightly posterior to the AV node"
and explain why we have a second way to stimulate the lower parts of the heart even though it can and does cause the very problems as I noted when two differnent systems can cause the heart to contract."
It is possible for the brain signal intended to trigger one shot from the AV node is too weak or non-existent. Thus nature has provided an alternative way to keep the heart beating at least at a slower rate. If it has been too long since the normal AV node was activated, then within the AV is another self activating single pulse generator but not strong enough by its self to cause the ventricle parts of the heart to contract. Thus as this backup generator is below the AV node, it sends it signal retrograde to trigger the needed stronger AV node half cycle of that one-shot oscillator and keep you from dying.
Perhaps an analogy will help: We put life boats on ship in case something goes wrong, but they can cause something to go wrong. For example in a storm, the ropes holding one end of the life boat can break allowing it to swing free and punch some holes in the hull so that the storm's larger waves enter making ship float lower and fill with water faster until it sinks. Before that happens, the captain will order it cut free. Life boats, even though part of the ship are not a parallel floatation system, but a backup system to be used SEQUENTIALLY if the primary system fails.
AVNRT is caused by a backup system than often saves lives, but if the backup pulse to the AV node is not needed as brain is triggering the AV node OK, and the backup system is active too, then you have two systems trying to control the heart's beating. Best to destroy one - the backup one (Ablate it, with well localized heating as it is distinct tissue like the life-boats are. Laser heating is used now days, I think). AVNRT seldom kills but will if it converts to ventricular fibrillation* as it often does if the AVNRT is not just a few cycles of heart beat rhythm - last for a minute or so.
Thanks for directing me to link that illustrates well how two different systems trying to control heart beat is NOT nature's plan. - Do not exist in the brain as I stated. That does not rule out backup systems which do exist - at least three for heart beat.
*BTW my group at APL/JHU made a much larger implanted device that could terminate automatically ventricular fibrillation. I did not work on that project but followed it closely. MedTrons also sells that APL designed device. We called it AID, for Automatic Implantable Defibrillatior, but after AIDs had a differnent meaning, MedTronics renamed it. It would try three times to stop the ventricular fibrillation. Gave each internally delivered shock about 10 seconds apart as we had to recharge the energy storage capacitors. This meant by standers would see the victim convulsing three times.
We knew lawyers would fight each other for the right to claim APL had killed him; so we included a "bucket memory" - several times each second the data in bucket n transferred to bucket n+1 and eventually was lost as the last bucket in the chain got new data. - We could proof in court that victim was in ventricular fibrillation 5 seconds before our device tried even the first of three times to save him. In that era, this added to the cost and volume. We did not want to tell real reason it was needed** - So said it was for medical research - provided EKG data for 5 or so seconds before ventricular fibrillation began.
** No doctor would implant one and no company would make one without that bucket memory, as quiet often the victim of ventricular fibrillation does die - even with automatic intervention in a few seconds. They did not want many dozens of multi-million dollar law suits each year. In airport hall way you can see ventricular defibrillation boxes now. I would not use one on anyone - I'm not a doctor. Only a doctor, with stethoscope,*** would stand a chance of not losing very cent he had if the victim did not live. - That is the world we live in today: Of the lawyers, for the lawyers and by the lawyers. (You can replace "lawyer" with "very rich" to be more general.)
*** And a dam good, expensive lawyer with hours of documentation on sexy Power Point slides about ventricular fibrillation.