Fractal-AIMAS synergy for multiscale consciousness modeling in neuro-cybernetic systems: A multifractal, Kuramoto oscillator, and hybrid neuroprosthetic approach

Abstract

This paper introduces a novel framework for modeling conscious states by integrating fractal decomposition theory with Autonomous Intelligent Multi-Agent Systems (AIMAS) in brain-cyborg interfaces. The approach employs multifractal analysis (including Hausdorff dimension and MF-DFA) and Iterated Function Systems (IFS) to decompose hybrid neuro-silical architectures into scale-invariant components, revealing hierarchical and self-similar patterns in functional connectivity. Within the AIMAS architecture, consciousness is conceptualized as a self-organizing fractal attractor, where agents act as fractal feature extractors, coupled via Kuramoto oscillators over scale-free Koch networks. The system dynamics are modeled using stochastic partial differential equations (SPDEs), while distinct conscious states (e.g., wakefulness vs. anesthesia) are characterized using Lyapunov exponents and lacunarity-based strange attractors. Experimental validation is conducted using ECoG and neuroprosthetic datasets, along with synthetic Local Field Models (LFMs), benchmarked against LSTM and Transformer architecture. The fractal-AIMAS synergy paradigm is capable of exceeding 100 % admissibility of high-fidelity neuro-cybernetics in both performance and optimality.