The universal mathematical models of memristor, meminductor and memcapacitor are designed respectively, and based on these models, a simple parallel chaotic system is constructed. The dynamic characteristics of the system including phase diagram, time domain diagram, Lyapunov index, power spectrum and poincare cross section are analyzed, and its hyperchaotic characteristics are proved. The influence of equilibrium point stability, system parameters and initial value on the system is further studied. And it is shown that the symmetry change of parameters will cause the corresponding symmetry change of system state, however, the initial value does not affect the state of the system under the condition of chaotic oscillation. Finally, the circuit is designed and realized by using Multisim, and the numerical simulation results are in good agreement with the experimental results, which proves the practical feasibility and actual existence of the system. This work not only extends the application of memory element in the nonlinear category, but also makes the basic work for the practical application of memory element based hyperchaotic system.