Here are some signs that may indicate that the cat or dog is suffering from an anxiety disorder:

Signs for dogs:
Neurotic behavior:

Excessive licking of themselves, objects or people.
Chasing a tail or other objects.
Shaking or shaking:

Unexplained tremors or tremors in the body, especially during stressful situations.

Excessive barking:

Frequent or loud barking, especially when alone or during thunderstorms.
Frustration or anguish of separation:

Behaviors such as digging, tearing things, or defecating at home when they are alone.
escape:

Trying to run away from home or the environment when they feel anxious.
lack of appetite:

Eating little or not being interested in food in times of stress.
Change in social behavior:

Isolation or unwillingness to demand responses from other humans or animals.

Signs for cats:
Restless behavior:

Constant walking or looking for hiding places.
concealment:

Prolonged hiding in different places in the house.
Excessive licking or self-treatment:

Excessive self-licking or self-injury due to stress.
Change in appetite:

Tongue eating or lack of appetite during stressful situations.

unusual sounds:

Howling or other unusual sounds during stressful situations.
Changes in social behavior:

Lack of interest in interacting with humans or other animals.
Improper use of a litter box:

Defecating in inappropriate places as a result of stress.
If you recognize one or more of these signs in your cat or dog, it is recommended that you contact a veterinarian or pet behaviorist for proper advice and treatment.