Delayed Feedback Chaotification Model and Its Hardware Implementation

To solve the ubiquitous problems of frail chaos and dynamical degradation, a delayed feedback method is proposed in this article to construct hyperchaotic maps. In this method, the delayed feedback control increases the complexity, dimension, and period length of a chaotic map, and the use of modular operation for boundary control further improves its chaotic range and ergodicity. Taking three 1-D chaotic maps as seeds, some new high-dimensional chaotic maps are proposed based on this method. The chaotic properties of the proposed maps are analyzed by the definition of Lyapunov exponent (LE) and stability analysis. Performance evaluations show that the proposed maps have large chaotic ranges, positive LEs, hyperchaotic behavior, high complexity, uniform distribution, multiple coexistence attractor, and strong resistance to parameter estimation and dynamical degradation. To further verify its practicability, the proposed maps are implemented on a field-programmable gate array platform, and applied to the pseudorandom number generator and image compression.