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The dynamics on a chaotic attractor can be quite heterogeneous, being much more unstable in some regions than others. Some regions of a chaotic attractor can be expanding in more dimensions than other regions. Imagine a situation where two…
Chaos is generic in strongly-coupled recurrent networks of model neurons, and thought to be an easily accessible dynamical regime in the brain. While neural chaos is typically seen as an impediment to robust computation, we show how such…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often…
Improving the accuracy of forecast models for physical systems such as the atmosphere is a crucial ongoing effort. Errors in state estimation for these often highly nonlinear systems has been the primary focus of recent research, but as…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…
Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godel's…
Large language models (LLMs) often exhibit unexpected errors or unintended behavior, even at scale. While recent work reveals the discrepancy between LLMs and humans in skill compositions, the learning dynamics of skill compositions and the…
We propose a novel approach to generate chaotic business cycles in a deterministic setting. Rather than producing chaos endogenously, we consider aggregate economic models with limit cycles and equilibriums, subject them to chaotic…
Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…
A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene…
The apparantly irregular (unpredictable) space-time fluctuations in atmospheric flows ranging from climate (thousands of kilometers - years) to turbulence (millimeters - seconds) exhibit the universal symmetry of self-similarity.…
For applications of machine learning in critical decisions, explainability is a primary concern, and often a regulatory requirement. Local linear methods for generating explanations, such as LIME and SHAP, have been criticized for being…
We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Simulation results show that "weak chaos" exponent may be one of the characteristic exponents of the…
Estimating population models from uncertain observations is an important problem in ecology. Perretti et al. observed that standard Bayesian state-space solutions to this problem may provide biased parameter estimates when the underlying…
When training autoregressive models to forecast dynamical systems, a critical question arises: how far into the future should the model be trained to predict? Too short a horizon may miss long-term trends, while too long a horizon can…
Chaos reveals a fundamental paradox in the scientific understanding of Complex Systems. Although chaotic models may be mathematically deterministic, they are practically non-determinable due to the finite precision, which is inherent in all…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
The relationship between chaos and quantum mechanics has been somewhat uneasy -- even stormy, in the minds of some people. However, much of the confusion may stem from inappropriate comparisons using formal analyses. In contrast, our…