Fatemeh Helen Ghane

We investigate a six-dimensional (6D) dual-oscillator optomechanical system, where two mechanical resonators couple to a single optical mode, and show that noise acts as a control parameter that both accelerates the route to chaos and generates riddled basins —fractal intermingling of synchronized and anti-synchronized attractors. Combining Poincaré sections, 2D/3D phase-space projections, the full Lyapunov spectrum, Kaplan–Yorke dimension, Melnikov analysis, and Fokker–Planck diagnostics, we obtain a quantitative and self-consistent picture of noise-induced complexity. As the laser drive increases, a Feigenbaum-type period-doubling cascade culminates in chaos and hyperchaos ( λ ₁ > 0; λ ₁ , λ ₂ > 0 with D _KY ∈ [2, 4] ), while Melnikov predictions confirm homoclinic intersections underlying global instability. Riddled-basin formation is demonstrated and quantified by a stability index σ = 0.3–0.6, (ii) fractal basin dimension D _B ≈ 1.2–1.55, and (iii) basin entropy S _B ≈ 0.3–0.45, all peaking in the noise-driven regime. Transverse Lyapunov exponents along the synchronized and anti-synchronized attractors remain negative (transverse stability), while transversely unstable periodic orbits embedded in the attractors provide the dynamical mechanism for riddling. A critical noise threshold D _c ≈ 0.05 is identified for attractor switching and the smearing of bifurcation structure; largest-exponent maps λ ₁ ( E , D ) correlate these transitions with parameter space. Our results establish rigorous evidence for noise-modulated (hyper)chaos in high-dimensional optomechanics and offer predictive levers (detuning, coupling, and noise engineering) for controlling instability in microcavity and LIGO-type platforms, as well as enabling applications in chaos-based photonics and sensing.

In order to effectively manage infectious diseases, it is crucial to understand the interplay between disease dynamics and human conduct. Various factors can impact the control of an epidemic, including social interventions, adherence to health protocols, mask-wearing, and vaccination. This article presents the development of an innovative hybrid model, known as the Combined Dynamic-Learning Model, that integrates classical recurrent dynamic models with four different learning methods. The model is composed of two approaches: The first approach introduces a traditional dynamic model that focuses on analyzing the impact of vaccination on the occurrence of an epidemic, and the second approach employs various learning methods to forecast the potential outcomes of an epidemic. Furthermore, our numerical results offer an interesting comparison between the traditional approach and modern learning techniques. Our classic dynamic model is a compartmental model that aims to analyze and forecast the diffusion of epidemics. The model we propose has a recurrent structure with piecewise constant parameters and includes compartments for susceptible, exposed, vaccinated, infected, and recovered individuals. This model can accurately mirror the dynamics of infectious diseases, which enables us to evaluate the impact of restrictive measures on the spread of diseases. We conduct a comprehensive dynamic analysis of our model. Additionally, we suggest an optimal numerical design to determine the parameters of the system. Also, we use regression tree learning, bidirectional long short-term memory, gated recurrent unit, and a combined deep learning method for training and evaluation of an epidemic. In the final section of our paper, we apply these methods to recently published data on COVID-19 in Austria, Brazil, and China from 26 February 2021 to 4 August 2021, which is when vaccination efforts began. To evaluate the numerical results, we utilized various metrics such as RMSE and R-squared. Our findings suggest that the dynamic model is ideal for long-term analysis, data fitting, and identifying parameters that impact epidemics. However, it is not as effective as the supervised learning method for making long-term forecasts. On the other hand, supervised learning techniques, compared to dynamic models, are more effective for predicting the spread of diseases, but not for analyzing the behavior of epidemics.

Addendum and corrigendum to "On the chaos game of iterated function systems"

In this paper, we present a novel synchronization method for chaotic systems—the so-called parallel synchronization method. The proposed technique provides a condition whereby an optimal control problem can be applied in order to achieve active control whenever we use an active control strategy for synchronization. In this way, by transforming the synchronization problem to an optimal control problem, we can define an appropriate error function such that by minimizing it while the active control is obtained, the synchronization error approaches zero. Some different chaotic systems are considered for synchronization, and the numerical simulations are presented graphically to confirm the validity of the proposed method.