A four-dimensional memristive system is constructed using a novel ideal memristor with cosine memductance.Due to the special memductance nonlinearity,this memristive system has a line equilibrium set (0,0,0,δ) located along the coordinate of the inner state variable of the memristor,whose stability is periodically varied with a change of δ.Nonlinear and one-dimensional initial offset boosting behaviors,which are triggered by not only the initial condition of the memristor but also other two initial conditions,are numerically uncovered.Specifically,a wide variety of coexisting attractors with different positions and topological structures are revealed along the boosting route.Finally,circuit simulations are performed by Power SIMulation (PSIM) to confirm the unique dynamical features.