  We theoretically analyze the entanglement generation and dynamics by coupled
Josephson junction qubits. Considering a current-biased Josephson junction
(CBJJ), we generate maximally entangled states. In particular, the entanglement
dynamics is considered as a function of the decoherence parameters, such as the
temperature, the ratio $r\equiv\omega_c/\omega_0$ between the reservoir cutoff
frequency $\omega_c$ and the system oscillator frequency $\omega_0$, % between
$\omega_0$ the characteristic frequency of the %quantum system of interest, and
$\omega_c$ the cut-off frequency of %Ohmic reservoir and the energy levels
split of the superconducting circuits in the non-Markovian master equation. We
analyzed the entanglement sudden death (ESD) and entanglement sudden birth
(ESB) by the non-Markovian master equation. Furthermore, we find that the
larger the ratio $r$ and the thermal energy $k_BT$, the shorter the
decoherence. In this superconducting qubit system we find that the entanglement
can be controlled and the ESD time can be prolonged by adjusting the
temperature and the superconducting phases $\Phi_k$ which split the energy
levels.
