Chaos–Counter-Chaos Theory: Emergent Harmonic Regime and Tri-Dynamic Competitive Systems (Version 1.3)

Title: Chaos–Counter-Chaos Theory: Emergent Harmonic Regime and Tri-Dynamic Competitive Systems (Version 1.3) Author 1: Hau Dinh Thai Affiliation: Independent Theoretical Researcher , Author 2: GPT-5.2 Affiliation: Collaborative Development Description Version 1.3 of the Chaos–Counter-Chaos Theory introduces a third dynamic component termed the Harmonic regime, which mediates interactions between chaotic and counter-chaotic processes. The theory proposes that complex systems may operate either in dual-dynamic mode governed by Chaos–Counter-Chaos interactions or in tri-dynamic mode where a Harmonic regime emerges under sufficient disturbance conditions. A conceptual and mathematical framework is presented using nonlinear differential equations, probabilistic regime dominance, stability analysis, and triangular phase-space representation. The framework provides a generalized model for understanding interactions between instability, stabilization, and mediation across physical, biological, and social systems. , Version: 1.3 , Keywords: 1. Chaos dynamics2. Counter-chaos systems3. Harmonic regime4. Tri-dynamic systems5. Nonlinear dynamics6. Complex adaptive systems7. Regime competition8. Dynamic equilibrium9. Systems theory