How does Napoleon use fear to stay in power?

In Animal Farm, Napoleon implements a variety of methods to put fear in the other animals in order to maintain power. He scares the animals by both mental and physical means Once Mr. Jones and the humans are removed from the farm, he consistently uses the idea of Mr. Jones coming back as a way of ensuring that the animals do as he says. In this case, Napoleon places fear mentally on the animals, as they believe that Mr. Jones coming back would be to their detriment.
Additionally, Napoleon physically instills fear in the animals by abusing those who go against his word. Napoleon strategically separates himself from the rest of the group, and raises the puppies to conduct violent acts for him. In Chapter 7, he demonstrates his willingness to incite violence on the animals when he attacks the hens who questioned his methods. As all the animals watch, Napoleon has established his total authority in which all the animals now understand that rebelling against him will result in physical harm, or potentially death.
Through both the instilling of fear of ideas and fear of physical safety, Napoleon uses brainwashing and violent methods to maintain his power over the animals in Animal Farm.

In Animal Farm, Napoleon uses fear to crush any opposition to his regime. We see this clearly in Chapter 5 when Napoleon uses fear to expel Snowball from the farm. When he realizes that Snowball's plans for the windmill are very popular with the animals and that he may lose the vote, he sets his attack dogs on Snowball and forces him off the farm. By doing this, Napoleon sends a clear message, not only to Snowball, but also to the other animals, that anyone who disagrees with him will be removed by force.
Similarly, when the hens rebel against him in Chapter 7, Napoleon acts "swiftly and ruthlessly." Once again he uses the fear of violence (through the threat of death) to force the hens into agreeing to his policy of selling their eggs.
Napoleon, therefore, uses fear through the threat of violence to ensure that the animals agree with his policies. By doing this, Napoleon is able to maintain his power on the farm.