Chaos Theory

Chaos, Ito-Stratonovich dilemma, and topological supersymmetry ArXiv ID: 2512.21539 “View on arXiv” Authors: Igor V. Ovchinnikov Abstract It was recently established that the formalism of the generalized transfer operator (GTO) of dynamical systems (DS) theory, applied to stochastic differential equations (SDEs) of arbitrary form, belongs to the family of cohomological topological field theories (TFT) – a class of models at the intersection of algebraic topology and high-energy physics. This interdisciplinary approach, which can be called the supersymmetric theory of stochastic dynamics (STS), can be seen as an algebraic dual to the traditional set-theoretic framework of the DS theory, with its algebraic structure enabling the extension of some DS theory concepts to stochastic dynamics. Moreover, it reveals the presence of a topological supersymmetry (TS) in the GTOs of all SDEs. It also shows that among the various definitions of chaos, positive “pressure”, defined as the logarithm of the GTO spectral radius, stands out as particularly meaningful from a physical perspective, as it corresponds to the spontaneous breakdown of TS on the TFT side. Via the Goldstone theorem, this definition has a potential to provide the long-sought explanation for the experimental signature of chaotic dynamics known as 1/f noise. Additionally, STS clarifies that among the various existing interpretations of SDEs, only the Stratonovich interpretation yields evolution operators that match the corresponding GTOs and, consequently, have a clear-cut mathematical meaning. Here, we discuss these and other aspects of STS from both the DS theory and TFT perspectives, focusing on links between these two fields and providing mathematical concepts with physical interpretations that may be useful in some contexts. ...

Chaotic Bayesian Inference: Strange Attractors as Risk Models for Black Swan Events ArXiv ID: 2509.08183 “View on arXiv” Authors: Crystal Rust Abstract We introduce a new risk modeling framework where chaotic attractors shape the geometry of Bayesian inference. By combining heavy-tailed priors with Lorenz and Rossler dynamics, the models naturally generate volatility clustering, fat tails, and extreme events. We compare two complementary approaches: Model A, which emphasizes geometric stability, and Model B, which highlights rare bursts using Fibonacci diagnostics. Together, they provide a dual perspective for systemic risk analysis, linking Black Swan theory to practical tools for stress testing and volatility monitoring. ...

Transformers Beyond Order: A Chaos-Markov-Gaussian Framework for Short-Term Sentiment Forecasting of Any Financial OHLC timeseries Data ArXiv ID: 2506.17244 “View on arXiv” Authors: Arif Pathan Abstract Short-term sentiment forecasting in financial markets (e.g., stocks, indices) is challenging due to volatility, non-linearity, and noise in OHLC (Open, High, Low, Close) data. This paper introduces a novel CMG (Chaos-Markov-Gaussian) framework that integrates chaos theory, Markov property, and Gaussian processes to improve prediction accuracy. Chaos theory captures nonlinear dynamics; the Markov chain models regime shifts; Gaussian processes add probabilistic reasoning. We enhance the framework with transformer-based deep learning models to capture temporal patterns efficiently. The CMG Framework is designed for fast, resource-efficient, and accurate forecasting of any financial instrument’s OHLC time series. Unlike traditional models that require heavy infrastructure and instrument-specific tuning, CMG reduces overhead and generalizes well. We evaluate the framework on market indices, forecasting sentiment for the next trading day’s first quarter. A comparative study against statistical, ML, and DL baselines trained on the same dataset with no feature engineering shows CMG consistently outperforms in accuracy and efficiency, making it valuable for analysts and financial institutions. ...

Stock Price Prediction using Dynamic Neural Networks ArXiv ID: 2306.12969 “View on arXiv” Authors: Unknown Abstract This paper will analyze and implement a time series dynamic neural network to predict daily closing stock prices. Neural networks possess unsurpassed abilities in identifying underlying patterns in chaotic, non-linear, and seemingly random data, thus providing a mechanism to predict stock price movements much more precisely than many current techniques. Contemporary methods for stock analysis, including fundamental, technical, and regression techniques, are conversed and paralleled with the performance of neural networks. Also, the Efficient Market Hypothesis (EMH) is presented and contrasted with Chaos theory using neural networks. This paper will refute the EMH and support Chaos theory. Finally, recommendations for using neural networks in stock price prediction will be presented. ...