Chaotic System with Zero Dissipation Measure on Centered Sphere

Abstract Autonomous third-order chaotic dynamical system with zero dissipation measure on centered sphere is discussed in this paper. Radius of this sphere represents one of system´s parameters. Starting from cyclically symmetrical vector field, algebraically the simplest form of mathematical description is obtained (at least so far, based on thorough literature review). Generated strange attractor is interestingly shaped, with significant degree of entropy, randomness, and long-term unpredictability. In frame of numerical investigation, dynamical behavior is quantified using concept of Lyapunov exponents, spectral and approximate entropy. To prove robustness of generated chaotic attractor, continuous-time system integration is demonstrated via flow-equivalent lumped electronic circuit design, construction, and experimental verification.