The verb emulate means to imitate someone or something because you admire them. It also means to attempt to equal or surpass someone especially by imitation.
Synonyms are mimic, mirror, follow, or contend.
The word is a back-formation from emulation, or it origins from Latin aemulatus, past participle of aemulari meaning “to rival”.
Their goal is to emulate the success of other online stores.
He’s eager to emulate Matthew’s record of three successive international awards.
They are all expecting me to emulate my professor’s teaching style.