Chaotification of Sine-series maps based on the internal perturbation model

In this paper, a chaotification method based on the internal perturbation model (IPM) is proposed. The single-perturbation and the multiple-perturbations are introduced. The Sine map is taken as an example. Moreover, this method can be generalized to high-dimensional maps that contain sine, no matter where the sine term is in the system equation. we further apply IPM to an integer-order and a fractional-order Sine-series map. For those new maps, the parameter space and FuzzyEn complexity are significantly extended while maintaining the topological structure of system. These complex behaviors and digital signal processing (DSP) implementation validate the effectiveness of IPM and make it have the potential of better secure communication and encryption.

Automated summary

This paper presents a chaotification method based on the internal perturbation model (IPM) which can be applied to various maps, with further research on integer-order and fractional-order Sine-series maps. IPM method expands parameter space and complexity while maintaining the system's topological structure, validating its effectiveness in digital signal processing.