A New Chaotic Jerk System with Cubic and Hyperbolic Sine Nonlinearities and Its Application to Random Number Generation and Biomedical Image Encryption

Document Type : Article


1 Department of Electronics and Communication Engineering, V.S.B. Engineering College, Karur, Tamil Nadu, India – 639111

2 Centre for Control Systems, Vel Tech University, 400 Feet Outer Ring Road, Vel Nagar, Avadi, Chennai-600062, Tamil Nadu, India

3 Department of Computer Engineering, Faculty of Engineering, Hitit University, Corum, 19030, Turkiye

4 Department of Electronics and Automation, Osmancık Omer Derindere Vocational School, Hitit University, Corum, 19500, Turkiye


In this research paper, a new chaotic jerk system is proposed, which is constructed using cubic and hyperbolic sine nonlinearities. A detailed dynamical analysis of the chaotic jerk system is presented with the bifurcation diagrams and Lyapunov exponent spectrums. The novelties of the proposed system are that it can exhibit bistability for two different initial conditions, amplitude control, and offset boosting control. We also carry out a detailed analysis of the amplitude control and offset boosting control for the proposed jerk system. Furthermore, a random number generator (RNG) is designed using the proposed chaotic jerk system. The study was developed in the Python-based Google Colaboratory environment. The obtained random numbers have successfully passed the NIST 800-22, FIPS140-1, and ENT statistical tests, and it has been shown that they can be used successfully in encryption areas. Biomedical image encryption application was carried out using the generated random numbers. Finally, the reliability of the encryption process has been proven by performing histogram, correlation, NPCR-UACI, and entropy analyses, key space analysis, key sensıtıvıty analysis, and robustness analyses.


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