Circuit Scheme for Observing Coexisting Behaviors in Discrete Systems

Discrete chaotic systems in simple algebraic forms show great potential in many fields due to their complex dynamics and coexisting behaviors. Recently, an analog circuit scheme for implementing discrete systems has been proposed, but this scheme cannot exhibit essential coexisting behaviors in discrete systems. To address this issue, this paper proposes a novel analog circuit scheme for experimentally observing the coexisting behaviors in discrete systems. A discrete memristor model and two discrete chaotic maps are taken as examples, and their analog circuits are designed and physically implemented. By appropriately setting the initial values, the pinched hysteresis loops related to the initial values of the discrete memristor model, the coexisting attractors of the discrete memristor map and the initial-offset-control coexisting behaviors of the discrete neuron model are simulated, respectively. In particular, the printed circuit board based on trigonometric chip, sample-and-hold device, operational amplifier chip, and other components is fabricated. The coexisting behaviors are observed experimentally, thus verifying the numerical simulations and circuit simulations. The proposed scheme provides a new framework for the physical realization of discrete systems.