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Linear dynamics, also known as hypercyclicity, examines the dynamics of linear operators on separable, infinite dimensional Banach spaces. Formally, an operator $T$ on a Banach space $X$ is hypercyclic if there exists a vector $x$ in $X$ for which its orbit $Orb(T, x) = \{T^nx:n\geq0\}$ is dense in $X$. In 2007, Bes and Peris, and Bernal-Gonzalez independently introduced the concept of disjoint hypercyclic. We say two linear operators $T_1, T_2$ are disjoint hypercyclic if there exists a vector $x$ in $X$ for which the orbit $Orb(T_1 \otimes T_2,(x, x)) = \{(T^n_1x,T^n_2x):n\geq0\}$ is dense in direct sum $X \otimes X$. In the present talk, we will compare the dynamical properties of traditional hypercyclicity with the newer disjoint hypercyclicity, and we will see that many of the standard dynamical properties of hypercyclic operators fail to hold true in the disjoint setting.