Multimodal Chaotification Model with Hardware Implementation

Designing chaotic maps with desired dynamic properties is an attractive but challenging task. Although a lot of efforts have been devoted, many existing chaotic maps still suffer from some problems such as the insufficient chaotic behavior, discontinuous chaotic range, and nonuniform sequence distribution, which may bring negative effects to the industrial applications based on them. To alleviate these problems, this article proposes a multimodal chaotification model (MCM), and it can generate many new 1-D enhanced chaotic maps by performing the specially designed geometric and linear operations on existing 1-D chaotic maps. Based on the Lyapunov exponent and Frobenius-Perron operator, MCM is analyzed, and a series of theorems and corollaries obtained theoretically proves its effectiveness. As examples, two new 1-D chaotic maps are generated by our MCM, and the numerical evaluations demonstrate their outstanding properties. At the same time, the experimental results of field-programmable gate array also show that they have good implementability on hardware devices. To show the potential of MCM in industrial applications, the illustrative chaotic maps are applied to pseudorandom number generator and image encryption, and our designed schemes achieve superior performance indicators.