Whether there should be a dot after a figure title (in a scientific book)? Note that I have figures numbered like "Figure 1. ..."
The example figure caption in section 5.23 (Figure Legends and Captions) of the 6th edition of the Publication Manual of the American Psychological Association is formatted as follows:
Figure 3. Fixation duration as a function of the delay between the duration of eye fixation and the onset of the stimulus in Experiment 1. (American Psychological Association, 2010)
From this we can see that there is a period in the figure caption both after the number and after the descriptive phrase. I suggest you check the style manual of whatever style you are following to make sure my example matches with that particular format.
Usually figure numbers are given consecutive numbers without the dot, or they are given chapter numbers with a dot to indicate which illustration it was in the chapter. For example, 2.3 would be the third figure in chapter two.
If the chapter is broken down into sections, the number becomes a three figure one e.g. 2.3.4 is chapter two, section three, figure four.
The figure number is an identifier or name if you will, so just as you don't automatically put a period after Bob every time it occurs the placing of punctuation after figure identifiers depends on where it is used in the sentence and ordinary rules of punctuation are used. The only exception is if the figure identifier directly precedes another numeral (which should be avoided at all costs) you may use additional punctuation to differentiate the two numbers, but it is better to reword.