Well basically, when i was exploring this morning i was on 80 EXP and hoping to find a cheetah lion or something to fight so i could lv up. So i used all my energy and gt nothing :/ while that happen i did think of something. When your exploring could there be a button next to it that says Roar? If we were to have it what it would do is call over any rival animals that want to fight you. For example:
I pressed the 'roar' button, pay 5 SB it takes a random amount of energy (like exploring dose but you pay the additional 5 SB) then throughout your entire other explore clicks it would boost up the chances of you bumping into another rival animal. Of course you wouldn't have to press it it would be optional. Do you guys like it? Or is it just me that likes to fight cheetahs and all the rest :)

EDITS:
@Alder Whisper ~ also attracts females
@Kraft {Asmita; CBC} ~ two buttons roar which attracts animals to fight and purr which attracts females
@Tau'ri~ one button 'Roar' (attracts enemies) 'grunt/puff' (attracts females)