PN is bounded but u can find there (2 0 0) < (2 0 1). So my question is. Am I wrong about boundedness of petri net or is something wrong with PT on the picture ?
Unboundedness can be studied from a fixed initial marking (=state). Then you want to find a state that is reachable, by firing transitions, but larger than the initial one.
You mention both states s1=(2,0,0) and s2=(2,0,1), which is in the picture. The problem is that I do not see how either one can be reached from the other.
So, start in the initial state, and analyse which transitions can be fired.
For the given Petri Net, the number of tokens for P_1,P_2 and P_3 is represented by m_1,m_2 and m_3 respectively. Based on the definition of boundedness of a Petri Net by Popova-Zeugmann (2013), the given Petri Net is bounded because m_1 ≤ 2,m_2 ≤ 2 and m_3 ≤ 2. In other words, there is a natural number (2 in this case) such that the number of tokens in P_1,P_2 and P_3 never exceeds the number.
I am also providing an example of an unbounded Petri Net and an example of a bounded Petri Net. Regardless of the initial marking, the Petri Net in Figure 1 is not bounded (or it is unbounded) because m_0 → ∞ when T_0 keeps firing.
For the given initial marking, the Petri Net in Figure 2 is bounded because m_0 ≤ 1 and m_1 ≤ 2. In general, the Petri Net in Figure 2 is bounded: let the initial value of m_0 = q_0 and the initial value of m_1 = q_1; m_0 ≤ q_0 and m_1 ≤ 2q_0+q_1
Popova-Zeugmann, L. (2013). Chapter 2 The Classic Petri Net [Electronic version]. Time and Petri Nets. Berlin; Heidelerg: Springer-Verlag.