Hyperchaotic Oscillator with Line and Spherical Equilibria: Stability, Entropy, and Implementation for Random Number Generation

Abstract

We present a hyperchaotic oscillator with two linear terms and seven nonlinear terms that displays special algebraic properties. Notably, the introduced oscillator features distinct equilibrium types: single-point, line, and spherical equilibria. The introduced oscillator exhibits attractive dynamics like hyperchaos with two wing attractors. To gain a better understanding, we provide the bifurcation and Lyapunov exponents. The Kolmogorov–Sinai entropy is applied to show the complexity of the oscillator. A microcontroller realization confirms the reliability of the oscillator. The proposed oscillator is successfully applied for RNG.

Keywords

• hyperchaos
• Poincaré cross section
• Kolmogorov–Sinai entropy
• bifurcation