As a new type of electronic components, a memristive device is receiving worldwide attention and can enrich the dynamical behaviors of the oscillating system. In this paper, we propose a 3D jerk system by introducing a generalized memristive device. It is found that the dynamical behaviors of the system are sensitive to the initial conditions even the system parameters are fixed, which results in the coexistence of multiple attractors. And there exists different transition behaviors depending on the selection of the parameters and initial values. Thereby, it is one important type of the candidate system for secure communication since the reconstruction of accurate state space becomes more difficult. Moreover, we build a hardware circuit and the experimental results effectively confirm the theoretical analyses.