A discrete second-order locally active memristor and its chaotic map: dynamical analysis and hardware implementation

Abstract Existing research on locally active memristors (LAMs) has primarily focused on first-order systems. Compared to classical first-order models, the core advantage of second-order memristors lies in the introduction of a second internal state variable, which enables more complex dynamical behavior and information processing capabilities than first-order memristors. This paper proposes a discrete second-order LAM (DSLAM). By coupling this novel memristor with a one-dimensional sine map, a three-dimensional chaotic map is constructed. Analysis of the Lyapunov exponent spectra and bifurcation diagrams confirms that this map exhibits enhanced chaotic properties compared with a two-dimensional chaotic map based on a discrete first-order LAM (DFLAM). Further dynamical analysis reveals that the new DSLAM chaotic map exhibits rich dynamical properties, high complexity, multiple coexisting attractors, and sensitivity to initial conditions. To validate the feasibility of DSLAM circuit implementation, a PSIM-based simulation circuit is designed, and a DSP-based digital hardware implementation is developed. The DSLAM proposed in this paper offers a new approach for extending LAMs to the second-order memristor, demonstrating improved dynamical characteristics and providing an effective pathway for DSLAM research.