Memristor-based systems can exhibit the phenomenon of extreme multi-stability, which results in the coexistence of infinitely many attractors. However, most of the recently published literature focuses on the extreme multi-stability related to memristor initial conditions rather than non-memristor initial conditions. In this paper, we present a new five-dimensional (5-D) two-memristor-based jerk (TMJ) system and study complex dynamical effects induced by memristor and non-memristor initial conditions therein. Using multiple numerical methods, coupling-coefficient-reliant dynamical behaviors under different memristor initial conditions are disclosed, and the dynamical effects of the memristor initial conditions under different non-memristor initial conditions are revealed. The numerical results show that the dynamical behaviors of the 5-D TMJ system are not only dependent on the coupling coefficients, but also dependent on the memristor and non-memristor initial conditions. In addition, with the analog and digital implementations of the 5-D TMJ system, PSIM circuit simulations and microcontroller-based hardware experiments validate the numerical results.

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