In this paper, a novel method is proposed for producing pseudo random numbers from differential equation-based chaotic systems. The proposed method utilizes a Lu-like chaotic system capable of exhibiting both Lorenz-like and Chen-like chaotic system behaviors for different parameter values. A parameter switching process controlled by a linear feedback shift register is used to obtain the transition between Lorenz-like and Chen-like behaviors. The system has a new initial condition for each transition. Thus, both the stabilization effect and the propagation of the integration errors that occur in the discretization of the differential equation-based chaotic systems are prevented. Additionally, the more complex behavior of the pseudo orbits in the phase plane makes future predictions difficult. The pseudo random numbers produced by the proposed method are tested with NIST SP 800-22 and TestU01 randomness test suites, and all tests are passed. The field programmable gate array implementation of the pseudo random number generator based on the proposed method is also presented, and the implementation results are compared with the implementation of a chaotic map-based pseudo random number generator.