Cascade-sine chaotification model for producing chaos

Motivated by the concept of cascade operator and sine enhanced model, this paper proposes a universal framework termed cascade-sine chaotification model (CSCM) for producing chaotic maps. The principle of the proposed method is to perform sine transformation on the outputs of the seed maps, and then cascade the results to construct new systems. Compared with one-dimensional (1D) nonlinear models, the CSCM can produce diverse chaotic maps with arbitrary dimensionality by combining existing seed maps. Moreover, the chaotic maps generated by CSCM possess extremely higher complexity and larger chaotic ranges than the seed maps. To verify the effectiveness of CSCM, four chaotic maps generated by CSCM are presented as examples, of which the dynamical properties are systematically analyzed. Simulation results indicate the generated systems perform robust hyperchaotic properties in a large parameter range. Finally, a pseudo-random number generator (PRNG) is introduced to investigate the practicability of CSCM and the test results demonstrate the randomness of the obtained chaotic sequences.

Automated summary

The paper proposes a universal framework called cascade-sine chaotification model (CSCM) for producing diverse chaotic maps with higher complexity and larger chaotic ranges compared to seed maps. The effectiveness of CSCM is verified through systematic analysis of four chaotic maps generated by CSCM, which exhibit robust hyperchaotic properties in a large parameter range. The randomness of the obtained chaotic sequences is demonstrated through the introduction of a pseudo-random number generator (PRNG) in the study.