Did you know that there are 51 plants native to North America with the word "sunflower" in their common name? There are 39 in the genus Helianthus (sunflower) and, thank goodness, only one with the common name "common sunflower" in our Native Plant Database. Happily, this USDA Plant Profile Map shows that it grows natively in Kimball County, NE. The reason we get into all this is that the soils, climate and rainfall can easily influence how abundantly any plant blooms in any year, and we didn't want to handicap ourselves by not knowing exactly where this plant was being cyclical. Here, from our webpage on this plant in our Native Plant Database, are the growing conditions for Helianthus annuus (Common sunflower):
Water Use: Medium
Light Requirement: Sun
Soil Moisture: Dry
CaCO3 Tolerance: Medium
Soil Description: Dry, disturbed clays or heavy sands.
Conditions Comments: Common sunflower spreads rapidly by seed, especially in disturbed sites. It has been shown to have an allelopathic effect on other plants. Many subspecies intergrade throught the species range. The cultivated giant sunflower is a member of H. annuus, derived through artificial selection."
Notice especially the line about "It has been shown to have an allelopathic effect on other plants." This means it protects its own territory by emitting substances to discourage competition from other plants. Because we could find no research-based answer to your question, we are going to make some suppositions. Like every plant, the sunflower is dependent on the weather (hot, cold, dry, wet) to thrive. When some of the numerous seeds put out by the sunflower (and not consumed by all the birds, insects and animals that love the seeds) in a very favorable place, it will first establish its dominance by trying to kill off all the other plants that like the same conditions. This will then permit it to make more blooms, drop more seed and take up new territory. In that sense, you could say it is cyclical. But if a year comes in which conditions are very bad for sunflowers, the other, less aggressive, plants may get a foothold and crowd out the sunflowers, so that would be seasonal.