A cougar is about four times as large as a bobcat. Every bobcat i have ever encountered runs away from an adult human.
However, it is rumored that cougars are returning to this area. The advice that i am aware of says that if you try to run away, the animal will pursue you, and likely can outrun you. you are better off to hold your ground and show dominance.
i used to live in a part of New Jersey where there were many bears. They hated loud noises. They would run away if you blew a whistle, or fired a gun. But never get between a mother bear and her cubs.
But a grizzly bear will eat you.