Disjoint hypercyclic weighted pseudoshift operators generated by different shifts

Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I$ . In this article, we characterize the disjoint hypercyclic and supercyclic weighted pseudoshift operators on $X$ in terms of the weights, the OP-basis, and the shift mappings on $I$ . Also, the shifts on weighted $L^{p}$ spaces of a directed tree and the operator weighted shifts on $\ell ^{2}(\mathbb{Z},\mathcal{K})$ are investigated as special cases.