Dynamic Analysis and Application of a Novel, Simple 4D Hyperchaotic Sprott-D System and a First Order Discrete Time Delta Sigma Modulator for E-Health

In this work, a Novel, simple 4D Hyperchaotic Sprott-D System extended from the well-known three-dimensional (3D) Sprott-D chaotic system proposed by Z. Wei in 2011 and a First order Discrete time Delta Sigma Modulator system are used to securely modulate two physiological signals for e-health applications. By incorporating a new dynamic variable and enhanced coupling structures, the proposed 4D system demonstrates hyperchaotic behavior, characterized by two positive Lyapunov exponents. Comparative analysis with the original Wei system and related literature underscores the advantages of the new model in terms of complexity, unpredictability, and potential applications in secure communication systems. Pseudo random bits are generated from the proposed new 4D Hyperchaotic system, successfully tested via NIST-800.22 test, and conveniently used in MATLAB Simulink software to encrypt and decrypt ECG and EEG signals in a reliable, confidential, simple and secure digital telemedicine system. Some standard metrics, such as key space analysis, key sensitivity, histogram and cross-correlation, are applied to verify the strength of the encryption scheme.