The Lancashire outfit have taken points from Manchester United, Manchester City, Tottenham and Chelsea so far this season, but still find themselves two points adrift of safety.
Second-placed Arsenal travel to Turf Moor on the back of seven consecutive wins, but Dyche is backing his players to rise to the occasion after beating Manchester City 1-0 and holding Tottenham to a goalless draw in their last two home games.
"I think it's like all the games, you've got to believe in what you do and the way you work and the players have got to show that when the whistle blows," he told the club's official website.
"I think we've done pretty well with that over the course of the season and our points tally against the superpowers and the more powerful teams has been reasonable for a club coming into this division.
"Obviously we understand the opposition the best we can and how they play and some of the work they try and do but we counter that with how we work.
"Certainly against Tottenham we made it very difficult for them and had chances to win the game and edged the game against Manchester City.
"I'm happy with the way the side is operating at the moment but it is a big challenge of course.
"They don't win those games by luck, because you can't win that many by luck and they're a very good side."
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