Multi-Basin Attractor Dynamics and Cosmic Flows in the Local Universe: An Analytical Formulation via Non-Markovian K-Kernel Potential

The large-scale structure of the universe is characterized by galaxies flowing towards local gravitational attractors, such as the Great Attractor and the Laniakea Supercluster. We present an analytical formulation for the effective gravitational potential of the local universe, incorporating the non-Markovian K-Kernel framework. The potential is modeled as a superposition of decaying Yukawa terms, representing local attractors, and a quadratic background term representing dark energy. This functional approach generates a complex topological landscape with multiple distinct basins. The simulation generates a 2D velocity field demonstrating that the K-Kernel memory mechanism naturally confines galaxies to local superclusters while preventing global collapse, offering a mathematically rigorous and novel geometric interpretation of cosmic flows.