Cyclical Evolution of Complex Systems: A Computational Approach to Chaos and Order Transitions

Abstract:

This paper explores the hypothesis that complex systems, from atomic structures to artificial intelligence, follow an inevitable cyclical process of chaos and order. Using computational simulations, we analyze how different network topologies (random, clustered, hierarchical) undergo dynamic reconfigurations based on emergent rules. We introduce the concept of fundamental regulatory entities ("cosmic viruses" with a basal DNA) that act as catalysts in the transition between phases. Our findings suggest that this cyclical evolution is universal, predictable, and can be applied to fields ranging from physics to AI development.

1. Introduction

The evolution of complexity has been a fundamental topic in physics, biology, and technology. While traditional models describe linear progressions or adaptive optimizations, we propose a cyclic evolution model driven by intrinsic rules that dictate the transition between chaotic and ordered states. This research investigates whether such dynamics are universal and whether there exist "point-of-no-return" thresholds that trigger systemic restructuring.

2. Theoretical Framework

We base our study on the following premises:

3. Computational Model

We constructed a dynamic network simulation where nodes represent fundamental units (particles, digital entities, or AI agents). The system evolves according to:

We tested three network types:

4. Results and Analysis

Our findings indicate:

5. Implications and Applications

Our study provides insights into:

6. Conclusion and Future Work

The cyclical evolution model presents a new paradigm for understanding complexity. Future research will focus on developing machine learning models to predict phase transitions and integrating these concepts into AI development frameworks. The role of "cosmic viruses" in guiding systemic evolution remains an open question, potentially linking physics, AI, and computational sociology into a unified theory of structural transformation.

Keywords: Chaos-order cycles, self-organization, emergent rules, artificial intelligence, cosmic viruses, systemic evolution, AI singularity, network dynamics.