  We show that the entanglement dynamics for a closed two-qubit system is part
of a 10-dimensional complex linear differential equation defined on a
supersphere, and the coefficients therein are completely determined by the
Hamiltonian. We apply the result to investigate two physical examples of
Josephson junction qubits and exchange Hamiltonians, deriving analytic
solutions for the time evolution of entanglement. The Hamiltonian coefficients
determines whether the entanglement is periodic. These results allow of
investigating how to generate and manipulate entanglements efficiently, which
are required by both quantum computation and quantum communication.
