Chaos-based image encryption: Review, application, and challenges

B Zhang, L Liu - Mathematics, 2023 - mdpi.com
Chaos has been one of the most effective cryptographic sources since it was first used in
image-encryption algorithms. This paper closely examines the development process of …

Bifurcations and loss jumps in RNN training

L Eisenmann, Z Monfared, N Göring… - Advances in Neural …, 2023 - proceedings.neurips.cc
Recurrent neural networks (RNNs) are popular machine learning tools for modeling and
forecasting sequential data and for inferring dynamical systems (DS) from observed time …

Causes of fragile stock market stability

L Gardini, D Radi, N Schmitt, I Sushko… - Journal of Economic …, 2022 - Elsevier
We develop a behavioral stock market model in which a market maker adjusts stock prices
with respect to the orders of chartists, fundamentalists and sentiment traders. We analytically …

Strange nonchaotic attractors in a class of quasiperiodically forced piecewise smooth systems

J Duan, Z Wei, G Li, D Li, C Grebogi - Nonlinear Dynamics, 2024 - Springer
The existence of strange nonchaotic attractors (SNAs) and the associated mechanisms are
studied in a class of quasiperiodically forced piecewise smooth systems. We show that the …

Spinning black holes with axion hair

C Burrage, PGS Fernandes, R Brito… - Classical and Quantum …, 2023 - iopscience.iop.org
In this work we construct and analyze non-perturbative stationary and axially-symmetric
black hole solutions in general relativity coupled to an electromagnetic and an axion field …

Identifying nonlinear dynamical systems with multiple time scales and long-range dependencies

D Schmidt, G Koppe, Z Monfared… - arxiv preprint arxiv …, 2019 - arxiv.org
A main theoretical interest in biology and physics is to identify the nonlinear dynamical
system (DS) that generated observed time series. Recurrent Neural Networks (RNNs) are, in …

The abatement game in a dynamic oligopoly: social welfare versus profits

D Buccella, L Fanti, L Gori, M Sodini - Annals of Operations Research, 2024 - Springer
This article considers an N-firm oligopoly with abating and non-abating firms and analyses a
dynamic setting in which the environmental regulator sets the tax rate to incentivise firms to …

Center bifurcation in the Lozi map

I Sushko, V Avrutin, L Gardini - International Journal of Bifurcation …, 2021 - World Scientific
We consider the well-known Lozi map, which is a 2D piecewise linear map depending on
two parameters. This map can be considered as a piecewise linear analog of the Hénon …

Perception of fundamental values and financial market dynamics: Mathematical insights from a 2D piecewise linear map

L Gardini, D Radi, N Schmitt, I Sushko… - SIAM Journal on Applied …, 2022 - SIAM
We develop a simple financial market model in which a market maker adjusts the price with
respect to orders placed by chartists and fundamentalists. A novel feature of our model is …

Currency manipulation and currency wars: Analyzing the dynamics of competitive central bank interventions

L Gardini, D Radi, N Schmitt, I Sushko… - Journal of Economic …, 2022 - Elsevier
Based on a behavioral exchange rate model, we show that a central bank that conducts
competitive interventions to promote its economy may devalue its currency, albeit at the …