Spider mites are more closely related to ticks and spiders than insects. They have the ability to produce silk on host plants. They are very tiny and very prolific.
An easy way to check for spider mites on your plant is to hold a white sheet of paper under the leaves and give the branch a sharp tap. If you see moving dark tiney specks on the paper, you have spider mites.
Dormant oils and insecticidal miticidal soaps can be applied to help control the population.