How does Wendy's character evolve in Peter Pan?

In J. M. Barrie's original story Peter Pan, Wendy Darling is presented as a young girl, presumably of 12 or 13 years of age, who is responsible, obedient, intelligent, and capable of caring for others, especially for her younger brothers, John and Michael.

When she meets Peter and goes to Neverland with him, she becomes more comfortable with being carefree and adventurous, and she isn't opposed to having fun; however, she's still reasonable, sensible and even takes on the role of "mother" to the lost boys.

Wendy exploring her childish side is certainly a way her character changes a little, or rather an opportunity for her to better understand herself and her true nature. The readers can see that, despite her acting more maturely than the other kids in Neverland, she's also just a kid herself.

The biggest change Wendy goes through, however, is her transformation from a child to an adolescent and eventually to an adult. Wendy realizes that she has to go back to her family and to the world of responsibilities and problems—she understands that she simply has to grow up. She comes to the conclusion that adulthood is not something one should fear but rather embrace. When she returns to London, she's wiser and more mature than she was before and ultimately grows up and has a child on her own.

Unlike Wendy, Peter never grows up and never changes—he remains the young, mischievous boy forever, refusing to enter the complicated world of adulthood.

In Peter Pan, how does Wendy's life change after interacting with Peter and the Lost Boys in Neverland?

After her adventures in Neverland, Wendy is a child on the brink of adolescence. She still delights in childish things and therefore accepts Peter's offer to clean house for him every spring. She is able to return to Neverland a few more times, though Peter does occasionally skip a year, forgetting all about Wendy. Eventually, his visits become more sporadic until they stop altogether. The more mature Wendy becomes, the less Peter seems to be drawn to her.

Even though she resists growing up at first, eventually Wendy begins to let go of Peter and Neverland as anything but a cherished childhood memory:

For a little longer she tried for his sake not to have growing pains; and she felt she was untrue to him when she got a prize for general knowledge. But the years came and went without bringing the careless boy; and when they met again Wendy was a married woman, and Peter was no more to her than a little dust in the box in which she had kept her toys. Wendy was grown up. You need not be sorry for her. She was one of the kind that likes to grow up. In the end she grew up of her own free will a day quicker than other girls.

Wendy's sense of responsibility, present even in childhood, becomes more predominant as she grows up. She becomes a wife and mother with a child of her own. When Peter returns, he has not changed, but Wendy very much has since she decided to grow up. Wendy becomes like Mrs. Darling then: she is responsible and must watch her own child Jane fly away with Peter to have adventures in Neverland of her own, showing that the story has come full circle.