Delay Difference Feedback Memristive Map: Dynamics, Hardware Implementation, and Application in Path Planning

The delay of state variable plays a crucial role in chaotic systems. However, it has not received sufficient attention in discrete memristor-based maps. This paper presents a study on the effects of delay feedback in the discrete memristive system, proposing a generalized delay difference feedback memristive map. The dynamical behaviors influenced by control parameters, delay length and initial conditions, are explored through four discrete memristive maps. The Kaplan-Yorke dimension is utilized as an indicator to investigate the chaotic dynamic variations induced by the delay length within memristive maps. Furthermore, digital circuits for the proposed systems are designed and implemented, with hardware experimental results that are consistent with numerical simulations, thereby verifying the effectiveness of the digital circuit-based system and providing a foundation for hardware-based delay difference system design. Additionally, the chaotic series are integrated into the particle swarm optimization for tackling obstacle avoidance path planning. The superiority of the designed delay difference feedback memristive maps is highlighted through comparisons with several classical chaotic maps, showcasing their enhanced performance in terms of the speed and cost efficiency in solving the path planning task.