Re: How the 2 ovaries coordinate to release only one egg in a single cycle?

Quoting from the chapter title, The Ovary in the authoritative Reproductive Endocrinology by Samuel S.C. Yen and Robert B. Jaffe:

" ... For reasons not [yet] well understood ... rarely, more than one follicle ovulates and gives rise to a corpus luteum during each menstrual cycle. ... "

This chapter explains how follicles undergo maturation during several menstrual cycles under the influence of the follicle stimulating hormone (FSH) .

Again, quoting from Reproductive Endocrinology:

" . . . The interval between beginning maturation and completing ovulation of a follicle in a given cycle is unkown. Specifically, it is not known whether maturation of that follicle begins during one or more cycles in advance of the in which it ovulates. However, a minimum figure for the time required for a follicle to mature to the point of ovulation can be deduced from the fact that that ovulation induction requires 10 to 12 days of preovulatory stimulation with exogenous [i.e., externally administered] gonadotropin [e.g., FSH] in women whose ovaries contain only primary follicles ..."

Let's now consider the case of what is called superovulation . This is where more than one follicle is deliberately produced artificially in women who do not ovulate normally; or who submit to artificial in vitro fertilization for overcoming some infertility problem involving the male and female couple. There is a complete explanation of how multiple ova are medically induced for deliberately causing superovulation.

The procedure is very carefully controled and monitored because manipulation of the ovarian follicles with administration of hormones requires critical timing and synchronization with the natural biological timing of the ovaries. Thus:

"... [hormones] are administered beginning on the second or third cycle day, and given for six to nine consecutive days. Response to these drugs is monitored by frequent vaginal ultrasounds and blood estrogen determinations. At a time in the cycle when the ovarian follicles reach a designated size, and estrogen levels are appropriate, an injection of the hormone HCG is given to trigger ovulation. Ovulation usually occurs 36-48 hours after the HCG injection. ..."

Although the above does not directly answer your simple question, perhaps it can provide some perspective as to why the answer is not an easy one to answer. Ovulation is a complex process for which the entire mechanism has not yet been worked out.