Now, What behavior can DFA, NFA etc simulate(mimic/imitate) of each other? What do we mean by their “behavior” ?

DFAs and NFAs are computational models that solve decision problems. By their “behavior”, we mean the language they recognize.

So, When we say that “an NFA can simulate a DFA”, we mean that if we have a DFA $D$ whose language(behavior) is $L(D)$ then we can have some NFA who also has same behavior(Language).

When we say that “a DFA can simulate an NFA”, we mean that if we have an NFA $N$ whose language(behavior) is $L(N)$ then we can have some DFA who also has same behavior(Language).

So, let’s ask two questions:

$\color{red}{\text{Can DFA be simulated with an NFA ?}}$

Answer : Obviously. Every DFA is a special kind of NFA. Thus if a language $L$ is recognized by a DFA $D$, then since $D$ is a special NFA, $L$ is also recognized by an NFA.

$\color{red}{\text{Can NFA be simulated with a DFA ?}}$

Yes. We can construct a deterministic finite automaton (DFA) to simulate the NFA $N$. For any NFA $N$, We can use the “set-of-states construction/Subset Construction/Powerset Construction” to get a DFA whose language is same as the NFA $N$.