In Hatchet, how do Brian's thoughts, feelings, and reactions change as a response to what has happened to him?

One way in which Brian's thoughts, feelings, and reactions change him is in his development of "tough hope."
When Brian is initially confronted with landing the aircraft, his thoughts center on how he is "gonna die." As he struggles to make sense of where he is and what he should do, Brian lacks the mental stamina to endure the perils of the wilderness. Brian's thoughts, feelings, and reactions help him develop a sense of internal strength, though. Brian begins this process by recalling the words of his teacher, Mr. Perpich, who would remind his students to approach challenges incrementally and that their own self-worth can help them face any situation bravely. From here, Brian develops a will to survive. For example, his reaction to the porcupine entering his shelter is to throw the hatchet against the wall, whereby sparks develop. From this, Brian learns how to make a fire. His experiences with needing to find food sources help him create different spears and weapons that he can use to hunt food. Brian emerges as a tower of mental fortitude in the way he deals with the tornado and moose attack. In each experience, Brian's thoughts, feelings, and reactions are geared towards surviving and enduring difficult times.
Over the course of the narrative, Brian develops a "tough hope," which demonstrates his commitment to survive the wilderness. His thoughts, feelings, and reactions show an unwillingness to be defeated:

He could feel new hope building in him. Not hope that he would be rescued—that was gone. But hope in his knowledge. Hope in the fact that he could learn and survive and take care of himself. Tough hope, he thought that night. I am full of tough hope.

Brian's "tough hope" transcends being rescued. It displays a resolve that he will survive. It represents how Brian's thoughts, feelings, and reactions have changed him.