MUMBAI, India, March 13 -- Intellectual Property India has published a patent application (202641024389 A) filed by Madhankumar C; Dr. P. Murugaiyan; Dr. C. Ramkumar; and Dr G Sheeja, Pollachi, Tamil Nadu, on March 1, for 'fractal-based stochastic modeling for ultra-complex multiscale mathematical systems.'
Inventor(s) include Dr. P. Murugaiyan; Dr. C. Ramkumar; and Dr G Sheeja.
The application for the patent was published on March 13, under issue no. 11/2026.
According to the abstract released by the Intellectual Property India: "Fractal-Based Stochastic Modeling for Ultra-Complex Multiscale Mathematical Systems Abstract Ultra-complex multiscale mathematical systems arise across diverse scientific and engineering domains, including turbulence dynamics, biological networks, financial markets, climate systems, and intelligent cyber-physical infrastructures. These systems exhibit nonlinear interactions, scale invariance, long-range dependencies, and inherent uncertainty that cannot be effectively captured by classical deterministic or single-scale stochastic models. This paper introduces a fractal-based stochastic modeling framework designed to represent and analyze ultra-complex systems operating simultaneously across multiple spatial and temporal scales. The proposed approach integrates fractal geometry, self similar processes, and stochastic dynamics to model scale-dependent randomness and emergent behaviors. By embedding fractal operators within stochastic differential formulations, the model captures non-Gaussian fluctuations, memory effects, and hierarchical coupling between micro-, meso-, and macro-level system components. Unlike conventional models that assume stationarity or linearity, the framework supports adaptive scaling laws and dynamically evolving probability distributions. A key contribution of this work is the formulation of multiscale fractal stochastic kernels that enable seamless transitions across scales while preserving structural complexity. The model demonstrates robustness in handling irregular data, chaotic regimes, and sparse observations, making it suitable for real-world ultra-complex systems. Analytical insights into stability, convergence, and scaling behavior are also discussed. The proposed fractal-based stochastic modeling paradigm provides a unified mathematical foundation for understanding, simulating, and predicting ultra complex multiscale phenomena. This work opens new research directions for advanced system analysis, intelligent modeling, and next-generation computational mathematics, particularly in environments where uncertainty, complexity, and multiscale interactions coexist intrinsically."
Disclaimer: Curated by HT Syndication.
