The London club fell off the top of the table last month after Manchester City thrashed them 6-3 and they were held to draws by Everton and Chelsea.
However, Arsene Wenger's side responded by beating West Ham, Newcastle United and Cardiff City in their last three top-flight games to return to the summit.
They also beat arch-rivals Tottenham in the third round of the FA Cup on Sunday and Rosicky, who was on target in that 2-0 victory, is bullish over their hopes of being crowned champions for the first time in a decade.
He told Arsenal's official website: "It was a bit bumpy when we lost against Manchester City and drew against Everton.
"But you will always have phases like that in a year so that's nothing new.
"This team has more experience than it did in the past. We have (Per) Mertesacker, (Mesut) Ozil, who won things in Madrid and the other experienced boys like Mikel (Arteta) and (Mathieu) Flamini.
"Plus the English boys are not kids anymore, they gained experience through the years of playing here so that's why I think we have the maturity to do it this year.
"The most important thing is that you never give up and always try to go for it,
"Like the game against West Ham, yes it will happen that the (other) team will score against you but you always have to carry on and that's what the boys did. It was very positive."
Arsenal received a timely boost this week as Alex Oxlade-Chamberlain returned to training after being sidelined since August with a knee injury.
Wenger will be hoping the midfielder is fit enough to feature in the first team before long with Theo Walcott ruled out for the rest of the season after damaging knee ligaments against Tottenham.
