  Chaos is associated with stochasticity, complex, irregular motion, etc. It
has some peculiar properties such as ergodicity, highly initial value
sensitivity, non-periodicity and long-term unpredictability. These pseudo
random features lead chaotic systems to enormous applications such as random
number generator, image encryption and secure communication. In general, the
concept of chaos is never associated with similarity. However, we found the
chaotic systems belonging to one chaos family (OCF) have similar dynamic
behavior, which is a novel characteristic of chaos.
  In this work, three classical chaotic system family are studied, which are
Lorenz family, Chua family and hyperbolic sine family. These systems contain
different derived chaotic systems (Lorenz system, Chen system and L\"u system),
different order chaotic systems (Chua family and hyperbolic sine family), and
different kinds of chaotic systems (chaos and hyper-chaos). Their PSPs
demonstrate that there exist strong correlation in OCF. Moreover, we found that
high order/dimensional chaotic systems will inherit all dynamic behavior of
lower ones, and the similarity will decrease as the order/dimensional goes
higher, which is analogous to genetic process in biology. All of these features
are quantitatively evaluated by PPMCC and SSIM.
