That's a tough one, because playing from behind in the jungle is really difficult, especially if the other jungler knows anything about counter-jungling. Plus being behind makes it so you wind up failing in situations that you would normally expect to succeed in (such as ganks or defending against invades).
The biggest think you can do is to try to keep up and not fall behind any further. The best way to do this is through vision and extremely careful counter-jungling. I'll explain:
The enemy jungler is going to try to farm camps and make plays around the map, and in order to remain as relevant as them in the game you need to be gaining something at the same time every time they attempt to do something.
Junglers get ahead by getting XP, gold, and by getting their laners fed. When you're behind, you can't realistically expect to be able to get gold and XP from making plays in lanes (unless something goes really in your team's favor of course) so you have to get it other ways and try to deny it from your opposing jungler as best you can.
You also don't want to fall any further behind (such as by dying) so avoid fights and confrontations with them as best you can. Keep the entrances to your own jungle (as well as the areas leading to lanes) warded and pay attention to the map so you can see if the enemy does try to do something sneaky. Getting counter-ganked or getting caught by surprise in your own jungle is the worst and it will happen to you when you're behind if you're not careful. Also, stay away from the enemy team's fed/farmed players unless you and your team significantly outnumber them - getting into a fight with them without it being a guaranteed win is just asking for something to go wrong and put you farther behind.
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Ward for your laners and constantly try to figure out where the enemy jungler is. By knowing where they are you can warn teammates when they attempt to set up ganks in your lanes and this way you can deny them the gold and XP they would have gotten from ganking that lane.
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Ward the entrances to your own jungle or get your allies to help you do so. Watch out for invades so that you can react accordingly (either collapse on them with your team or go counter-jungle or make plays elsewhere).
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If they show ganking a lane or invading your jungle, then you go and invade their jungle on the opposite side of the map, because if you can take a camp away before they get to it you will gain that gold and XP for yourself while denying it for them. If your blue side is being invaded, just go farm their blue side and avoid the potential fight entirely. Make sure to keep your wits about you, and be aware if any nearby enemy laners go missing, because if they do then they are most likely coming to kill you and you should leave.