Narrow Results

The concept of memory element or memory system is generalized to any device or system with memory effect in this paper. With the general definition of memory element, a new memory element model is proposed and its properties are studied. Based on the memory element, a simple chaotic memory system is constructed and its complex dynamics is depicted. These results verified by circuit experimental observations and PSIM simulations indicate that the proposed memory element has a pinched hysteresis loop characteristics for a periodic input, which depends on the initial state of memory element, and the amplitude and frequency of the applied input; the proposed chaotic memory system presents complex dynamics depending on system parameters and the initial state of memory element.

It is known that dynamical behaviors of memristive circuit are significantly affected by its initial states, which are difficult to be explicitly analyzed or controlled in voltage–current domain and have become great obstacles for its potential engineering applications. In this paper, the complex initial state-dependent dynamical behaviors of a physically realized memristive Chua’s circuit are detailed and investigated using incremental flux-charge modeling method. This circuit is modeled in terms of incremental flux and charge, in which the original line equilibrium point is converted into some determined equilibrium points relying on the initial states of the dynamic elements. Moreover, the special initial state-dependent behaviors are transformed into system parameter-associated behaviors. Consequently, the detailed influences of each initial state, even the occurrence of hidden oscillations, can readily be theoretically interpreted. Finally, the initial state-dependent behaviors are physically captured and directed in the equivalent realization circuit of the incremental flux-charge model.