A novel chaotic system with one absolute term: stability, ultimate boundedness, and image encryption

This paper proposes a system with an absolute term, exhibiting chaos. The system's dynamics are examined by computation of bifurcation and Lyapunov exponents. This system has a countable finite coexisting nested attractors. The features of the system make it suitable for secure applications. The system is combined with the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>4</mml:mn> <mml:mo>×</mml:mo> <mml:mn>4</mml:mn></mml:math> Toeplitz matrix to generate an encryption algorithm, validated using security and performance analysis. Combining the proposed system and the Toeplitz matrix improves the pixel distribution's randomness, significantly increasing security. The test results showed that the suggested image scheme is very secure and impervious to differential, statistical analysis, and other types of attacks. Furthermore, the majority assessment shows that the presented approach performs noticeably better than previous techniques.