I would say an example of man vs. self conflict in Twilight is Edward vs. himself. Because he has to fight against his thirst for Bella's blood to save his love for her.
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There is not much "man" vs "man" conflict in Twilight. This is because the two main male characters are a vampire and a werewolf.
There is more than one conflict in The Hobbit. The conflict with society would be with the river elves or Bilbo interactions with the dwarves as a group. But there is man vs man, man vs society, man vs enviroment
The external conflict in Lord of the Flies is when the kids themselves fight in a war with themselves. Another type of external conflict is when the kids bully Piggy and also when Ralph is being chased by Jack and his hunters. Jacob G.
Many people confuse man vs nature and man vs environment... Man vs environment is when man faces off against the natural world in which he lives - hurricanes, tidal waves, trapped on an island and has to survive (ex. Castaway, Blue lagoon, the Perfect Storm, one can argue the Titanic...) Man Vs Nature is man vs the nature of something - not mother nature. Trying to change the way something is. Good vs evil, for example. Good is good, and will always be good - evil is evil. Redemption stories often fall in this category. Several vampire stories or werewolf stories - (Angel, Twilight, Frankenstein, The devil vs daniel webster comes to mind, Hellboy) There are elements of man vs self depending on point of view - but if the hero uses the nature of his enemy against it, or is undone by the nature of his allies... Remember the story of the turtle and the scorpian ... the scorpian is at the side of the river and sees a turtle about to cross it - asks the turtle to give him a ride on his back. The turtle says "No, you'll sting me." The scorpian replies, "But, if I do, then we'll both drown." The turtle sees the logic in this, and agrees. About half way across the river, the Scorpian can't resist the temptation and stings the turtle. As they are both drawn under the waves the turtle asks, "But why did you sting me; now we'll both drown!" The scorpian replies "It is my nature."
When both Jack and Ralph stood as possible leaders Roger suggested that they should have a vote. The result was that Ralph was elected as leader and placed Jack in charge of the former choir as a consolation prize.
The concept of "man vs. self" is one in which the hero is facing an internal conflict against their own values or dreams. Some examples of this in film are "The Wrestler", "The Fly", "Fight Club" or "American History X", just to name a few.