Which stars brightness increases and declines?

Answer 1

Almost all stars are variable. over their lives (even the sun) however many stars are variable over a short period due to changes within the structure of the stars or from external influences. Examples of Eclipsing Binaries, Cepheid (type 1 and 2), RR Lyrae, OU Orionis etc.

Answer 2

Cepheid variables oscillate between two states: In one of the states, the star is compact and large temperature and pressure gradients build up in the star. These large pressures cause the star to expand. When the star is in its expanded state, there is a much weaker pressure gradient in the star. Without the pressure gradient to support the star against gravity, the star contracts and the star returns to its compressed state.

Answer 3

Many stars are what astronomers call "variables". Sometimes they are genuinely changing in brightness, sometimes it's a double star where one passes in front of another.

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Answer 4

Cepheid variables!