The given numbers in the series follows a pattern that,

Adding the corresponding numbers in first and last figures gives the corresponding number in the middle figure.

The logic in the given puzzle is 

Starting with the top 3 digit number, the first digit increases by 2 as you descend,from 1 to 11. The middle digit decreases by 1 each time,and the right hand digit alternates between 5 and 3

Looking at the diagram in  rows, the central circle equals half the sum of the numbers in the other circles to the left and right of the centre.

Starting with the 10 at the top, one set of numbers increases by 3 each time, written in alternate boxes as you move down the diagram, and the other set of numbers decreases by 2,written in the boxes remaining

In each row, 

Two series alternate here, with every third number following a different pattern.
In the main series, 4 is added to each number to arrive the next.
In alternate series, 5 is subtracted from each number t arrive the next number.
Here in the main series 
3 + 4 = 7
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19

In each circle, starting at the  top left segment ,numbers increase, as you move clockwise,by 2 for the upper left circle,3 for the upper right, 4 for the lower right and 5 for the lower left

Sum of all numbers in each row and columns must be 15.

Half the Product of Number in the upper & lower box gives the number in the middle box.

The given puzzle follows a pattern that,

Sum of numbers in all individual boxes must be equal.

In each circle,lower number equals the product of the top two numbers, subtracting 3 for the left hand circle, 4 for the middle, and 5 for the right hand circle.

Working in columns, the sum of the numbers in each column is always 14

Here in the given number puzzle, the given numbers follows a pattern that 

Let the value to be find be 'x'.

In each segment of the circle, multiply the outer two numbers together and subtract the sum of the outer two numbers in the opposite segment to give the value in the  inner grey segment

Given

Here in the given number puzzle, the logic is