Incremental integral reconstitution for detecting initial condition effects

The five-dimensional (5-D) two-memristor-based jerk (TMJ) system can emerge the initial condition-dependent extreme multi-stability due to two zero roots caused by its plane equilibrium set. However, using conventional stability analysis methods, we cannot explain the kinetic mechanism of initial condition effects on the 5-D TMJ system. To this end, this paper establishes a three-dimensional (3-D) incremental integral reconstructed (IIR) model using an integral transformation method, and converts the internal initial conditions and plane equilibrium set of the original system into the explicit initial condition parameters (ICPs) and one or no equilibrium point of the reconstructed model respectively. With the explicit ICPs and determined equilibrium point of the reconstructed model, the memristor and non-memristor initial condition effects on the original system are thereby detected by the stability distributions and then confirmed by the kinetic distributions. The results show that the memristor and non-memristor initial conditions have powerful influence on the kinetic effects of the 5-D TMJ system, and its kinetic mechanism of initial condition effects can be explained effectively based on the 3-D IIR model. Besides, with analog circuit and digital circuit platform, the circuit simulations and hardware experiments verify the kinetic effects of the ICPs on the 3-D IIR model.