  Exceptional point in non-Hermitian system possesses fascinating properties.
We present an exactly solvable attractor dynamics for the first time from a
two-level time dependent non-Hermitian Hamiltonian. It allows a way to evolve
to the coalescence state from a pure or mixed initial state through varying the
imaginary parameter along a specific diabatic passage. Contrast to a chaotic
attractor that is ultrasensitive to the initial condition, the designed
attractor is insensitive to the initial conditions. The attractor-like behavior
still exists for several adiabatic processes.
