Offset-Driven Symmetric Chaos Evolution for Path Optimization

Offset boosting enables spatial regulation of chaotic attractors, yet interactions among jointly regulated states and their computational value remain insufficiently explored. To connect correlated state regulation with intelligent search, this study develops a competitive offset regulation mechanism in a four-dimensional chaotic system. Numerical analysis reveals symmetric chaotic evolution, continuous attractor translation, and infinitely many homogeneous coexisting attractors. Competitive–compensatory interactions between the regulated states further enable coupling-dependent waveform overlap and separation. The principal dynamical behaviors are reproduced on an STM32H750 microcontroller, verifying the feasibility of digital implementation. To exploit the differentiated state information, single-state driving, fixed dual-state fusion, and adaptive regulation strategies are introduced to reconstruct the escaping-energy perturbation in Harris Hawks Optimization while preserving its original position-update mechanism. Comparative experiments and ablation studies demonstrate improved path quality and search stability in complex grid environments, particularly those containing narrow passages and multiple local optima. These findings connect competitive offset regulation with chaos-driven optimization and demonstrate the value of coordinated chaotic-state utilization for constrained path search.