Studying asymptotic behavior of bi-shadowing properties in multiple product dynamical systems in group space

In this paper, we presented a set of basic concepts in the group space, such as the definition of the bi-shadowing in its parameterized and unparameterized types. In the section three, we presented a set of theorems to study the bi-shadowing property of two dynamic systems, one of which is bi-shadowing and the other is (α,β)-bi-shadowing. In the section four, we studied the bi-shadowing property for a group space of dynamic systems that achieve the bi-shadowing property in two types mentioned.