Abstract
Continuous memristor has been widely used in chaotic oscillating circuits and neuromorphic computing systems. However, discrete memristor and its coupling discrete map have not been noticed yet. This article presents a discrete memristor and constructs a general two-dimensional memristive map model by coupling the discrete memristor with an existing discrete map. The pinched hysteresis loops of the discrete memristor are demonstrated. Four examples of memristive discrete maps are provided and their coupling strength-relied and memristor initial-boosted complex dynamics are investigated using numerical measures. The evaluation results manifest that the discrete memristor can enhance the chaos complexity and its coupling maps can generate hyperchaos. Particularly, the hyperchaotic sequences can nondestructively be controlled by memristor initial state and the initial-controlled hyperchaos is robust, which is applicable to many chaos-based applications. Additionally, we develop a hardware platform to implement the memristive maps and acquire the four-channel hyperchaotic sequences. We also apply the memristive maps to the application of secure communication and the experiments show that the memristive maps display better performance than some existing discrete maps.
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