I have found articles the try to give a possible biological neural network for the movement of limbs, neurons in the eyes, etc. Is there an explanation on how the neural network that controls the heart works?
The heart isn't really "controlled" by the nervous system in the same way, say, the limbs are. Heart muscle cells (cardiac myocytes) beat with a steady rhythm even in complete isolation. Collections of isolated cardiac myocytes will beat synchronously. The beating of the heart is controlled internally by two bundles of specialized cardiac myocytes, the sinoatrial node being the primary controller and the atrioventricular node regulating how the beat changes between the upper and lower chambers of the heart.
Although the heart beating it controlled internally, the nervous system does have an influence. This comes more generally from the sympathetic and parasympathetic nervous system, which control how our bodies respond to various levels of arousal and stress. These systems influence many parts of the body, but they influence the heart by "instructing" the sinoatrial node to alter its rate of beating. This is controlled primarily by the vagus nerve, if you are wondering about the specific neural anatomy. That nerve is involved in a wide variety of tasks, but it is particular important for the sympathetic and parasympathetic systems.