As the constraint imposed by the wave propagation condition limits the maximum allowed k //upshift (k // is the component of the wave vector parallel to the magnetic field), the lower hybrid wave (LHW) absorption is bounded in the region defined by the strong Landau-damping limit and the boundary of wave propagation domain. This absorption mechanism causes interplay of the distribution of the absorbed LH power with the modification of plasma configuration, which constitutes nonlinearity in the LHW propagation and absorption. The HL-2A discharge with LHW and neutral beam injected is modeled using the gyro-Landau fluid transport model, in which radiation is deliberately enhanced to modify the electron temperature. Because of the nonlinearity of the LHW propagation and absorption, the LH power deposition jumps from one stationary state to another through an intermediate unstable state, generating bifurcation in the LHW absorption. Onset of the LHW bifurcation closely correlates with the modification of electron temperature, showing that the change of the electron temperature is an essential ingredient in producing the bifurcation. The change of the current profile during the transition period between the two stationary LHW absorption states results in enhancement of the E×B shearing flow arising from toroidal rotation, which causes the shearing rate of E×B flow to exceed the growth rate of drift ballooning instability, triggering transport barrier development and achieving a steady internal transport barrier in the 2nd stationary LHW phase. It is suggested that a modification of electron temperature can be a plausible way to control the plasma confinement in the tokamak discharge with LHW injection.