Chaotic Dynamics in Vector Field Characterized by Spheres With Constant Divergence Measure

This paper contributes to discovering of continuous-time third-order autonomous deterministic chaotic system with predefined special property: homocentric spheres with constant vector field divergence measure. This kind of unique feature stands hidden within dynamics of system, i.e., it is not evident from a macroscopic point of view. Introduced mathematical model generates robust, topologically interesting, highly unpredictable, strange attractors. The way to new system was heuristic, based on nature-inspired optimization technique. Cyclical symmetricity of vector field selected at the beginning of system development process was followed by finding three free internal parameters that lead to chaotic behavior. Using both numerical analysis and experimental measurement, it is demonstrated that chaotic motion is robust and does not represent long transient or numerical artifact.