The phrase "by jerks" can be substituted with several different words that convey a similar meaning. One option is "sporadically," which refers to something that occurs in an irregular or infrequent manner. Another alternative is "intermittently," which suggests something happening with occasional breaks or pauses. If you want to emphasize the abrupt or jarring nature of the movement, you could use "jittery" or "choppy." Similarly, the word "staccato" implies short and sharp movements. Other synonyms include "fitfully," "unevenly," and "in spurts." When searching for the right term, consider the tone and context of your writing to ensure the substitution fits seamlessly.