Bocheng Bao,
Mo Chen,
School of Microelectronics and Control Engineering, Changzhou University, Changzhou, China
Abstract: The memristive circuit easily exhibits multi-stability or extreme multi-stability phenomenon with multiple or infinitely many coexisting attractors. Keeping the circuit element parameters unchanged and changing the initial conditions, the trajectory of the memristive circuit can asymptotically approach different operation states, showing the initial-condition-sensitive multi-stability phenomenon. These coexisting multi-stable states can provide more flexibility for the engineering applications of memristive circuits, but also pose new challenges to the traditional dynamical analyses and multi-stability control strategies. In the traditional mathematical models of the memristive circuits, the initial conditions are not explicitly expressed, which poses a barrier to the quantitative analysis of the multi-stability phenomenon. In addition, it is difficult to accurately control the initial values of dynamic components in the physical circuits, so the multi-stable operation modes can hardly be observed effectively. Using the flux-charge modeling method, we can realize the parameterized conversion of the initial conditions and achieve reconstitution of the multi-stability phenomenon. On this basis, the complex initial-condition-dependent dynamical behaviors and their formation mechanisms can be revealed and elaborated. Accurate prediction of multi-stable states and physical control of hardware circuits can be realized. The research results can provide theoretical guidance for the engineering applications of memristive circuits.