Complex dynamics of a bi-directional N-type locally-active memristor

This paper presents a bi-directional N-type locally-active memristor (LAM) model, which has two symmetrical locally-active regions with respect to the origin. For this memristor, the locally-active regions coincide with the edge of chaos regimes, where complex dynamic behaviors may occur. By deriving the small-signal admittance of the memristor, it is found that the LAM may be pure resistive, inductive or capacitive in terms of biasing voltages. When the LAM operates at the edge of chaos and connects with an external inductor in series, a second-order periodic oscillator is established. In this case, it is possible to move the poles of the system from the left-half plane to the right-half plane, thereby generating periodic oscillations. Complex dynamics of the second-order memristor-based oscillator is analyzed via Hopf bifurcation analysis and based on the theories of local activity and edge of chaos. Using the parasitic capacitor of the LAM in the second-order oscillator, a third-order chaotic oscillator is designed, which has a negative real pole and a pair of complex conjugate poles with positive real parts, satisfying the Shilnikov criterion. It is found that both periodic oscillation and chaos appear only at the edge of chaos of the LAM, thus verifying the complexity theorem, no-complexity theorem and edge of chaos theorem. Finally, circuit experiments are performed, which verify the dynamics and the effectiveness of the LAM model, the periodic oscillator and the chaotic oscillator.