Viet-Thanh Pham

Chaos and extreme events are characteristic manifestations of the complex and often unpredictable behavior of nonlinear dynamical systems. In this study, we introduce an oscillator capable of exhibiting both chaotic dynamics and extreme events. The proposed oscillator incorporates quadratic and absolute-value nonlinearities, which contribute to its rich dynamical behavior. A key feature of the system is the simultaneous availability of offset boosting and amplitude control without requiring changes in the initial conditions. By varying only the control parameter b, the oscillator exhibits a variety of dynamical regimes, including chaos and extreme events. Furthermore, bistability is demonstrated by varying the initial conditions, leading to the coexistence of distinct attractors for identical parameter values. An analog electronic circuit is designed to realize the proposed oscillator, demonstrating its feasibility for practical hardware implementation. The proposed system therefore provides a simple and flexible platform for investigating complex attractor dynamics, including chaos, extreme events, and bistability, while offering convenient control over the amplitude and offset of the generated signals.

With the rapid development of emerging technologies such as artificial intelligence, large models, data center networks, and the Internet of Things [1][2][3][4][5][6], the research on nonlinear systems and network systems is undergoing unprecedented changes and innovations. Nonlinear systems and networks remain the core pillars of modern applied physics and engineering. The extensive and indepth research conducted in recent years, ranging from chaotic systems to neural networks [7][8][9][10], chaotic circuits to memristive devices [11][12][13][14], complex systems and neuromorphic computing [15][16][17][18], traditional encryption applications to new ones [19][20][21][22][23], etc., those systems that violate the superposition principle continue to raise profound theoretical issues and give rise to practical solutions [24][25][26][27][28]. The Advances in Nonlinear Systems and Networks series, now in its fourth volume, serves as a dedicated forum for the latest developments in this field.This Research Topic brings together six original research articles spanning security analysis of chaos-based encryption, public opinion dynamics, bearing fault diagnosis, and parameter identification in chaotic synchronization. The breadth of contributions reflects both the maturity of nonlinear dynamics as a discipline and the persistent challenges that arise when theoretical results meet real-world signals, networks, and security requirements.The primary aim of this Research Topic is to present recent advances in the modeling, analysis, and application of nonlinear systems and networks. Nonlinear systems are characterized by the absence of superposition and uniformity in their input-output relationships, and they find wide application in engineering fields such as the Internet of Things, healthcare, and intelligent systems.The Topic encompasses nonlinear active and passive devices, nonlinear circuits and systems, memristors and neural circuits, memristive neurons and neural networks, complex systems and networks, control and synchronization, and their applications. The contributions in this volume address several of these themes, with a particular emphasis on signal processing and security in nonlinear environments.Physical layer encryption schemes offer flexible, low-cost protection for high-speed data transmission, but their security is often evaluated solely by key-space size. Wang et al. [29] address this gap by proposing a neural network-based attack scheme against physical layer chaos encryption. Their method learns effective ciphertext-to-plaintext mappings under fixed-key conditions, achieving sub-millisecond model-level inference after moderate offline training. The results demonstrate that the investigated Arnold-and Chen-based encryption schemes are vulnerable under the tested conditions, providing a complementary security-evaluation approach that moves beyond key-space metrics.Public opinion propagation exhibits nonlinear dynamics that traditional single-outbreak epidemic models fail to capture. Li and Hu [30] propose an enhanced SEIR-based model with two key mechanisms: transmission rates influenced by public attitudes and time-dependent immunity decay. The adjoint model quantifies opportunity costs of opinion control, enabling optimal control strategies. Compared to traditional models, their approach yields information diffusion peaks increased by 32% and peak arrival times delayed by 17.7%, with the public attitude amplification factor identified as a critical control node.Zhang et al. [31] proposed a super S2IR model based on hypergraphs to analyze the dissemination process of public opinion. The model introduced two types of disseminators with different motivations and capabilities, thereby systematically depicting the inherent heterogeneity of the dissemination group. The authors verified the theoretical conclusions through numerical simulations. Compared with traditional network structures, the hypergraph structure significantly accelerated the speed of opinion dissemination and expanded the scope of opinion dissemination. The research in this paper provides theoretical support and quantitative basis for analyzing the mechanism of public opinion dissemination and formulating intervention strategies.Two contributions address the challenging problem of extracting discriminative features from nonlinear signals for bearing fault diagnosis.Cheng et al. [32] propose an optimized matching feature extraction method based on reconstructed complete ensemble empirical mode decomposition with adaptive noise (RCEEMDAN) and an optimized mode-metrics matching (OMMM) strategy. RCEEMDAN reduces redundant modes in CEEMDAN, while OMMM determines the optimal matching relationship between decomposed modes and multi-source metrics. Experiments on chaotic signals and real bearing data verify superior classification performance compared with individual metrics. Dong et al. [33] introduce multivariate geometric entropy (mvGE) and its multiscale extension (mvMGE) for quantifying geometric complexity of multichannel bearing signals without selfparameters. Unlike single-channel geometric entropy, mvGE operates directly on the multidimensional space of multichannel signals, dispensing with time-delay embedding. The proposed method achieves classification accuracies of 97.9% and 95.1% on two independent bearing fault datasets.Zhang et al. [34] investigate information-optimal projection design for parameter identification in cross-order chaotic synchronization. They study an integer-order hyperchaotic master driving a lower-dimensional Caputo receiver through a rectangular projection. Reconstructing the projected regressor is equivalent to invariance of the projection kernel under every parameter matrix. Under fixed hardware noise and a nominal transmit-power constraint, the selected D-optimal design reduces held-out covariance volumes by factors of 12.6-18.2 relative to the median of 300 random feasible...

This paper introduces and studies the dynamic behaviors of a newly developed, memristor-based self-sustained van der Pol-Duffing oscillator system. The model is constructed from a basic self-governing circuit configuration with a diode pair by replacing the nonlinear components with a first-order memristive diode bridge. The Kirchhoff’s laws are applied to the circuit to derive its electrical state equations, which are modified to the dimensionless form. The equilibrium states of the model and their stability are analyzed. The dynamic behaviors of the model are studied with the help of phase portraits, bifurcation diagrams, Lyapunov exponents, and cross section of basin of attraction. Computational simulations demonstrate highly intricate and diverse operational regimes, exhibiting regular as well as chaotic trajectories, bubble-bifurcation, and multi-stability where distinct attractors coexist under identical parametric settings but varying initial states. A comparison between the proposed oscillator and ten other related systems featuring the same memristor model (a diode bridge cascaded with a first-order parallel RC filter) is presented. Remarkably, the proposed system achieves the lowest dimension and fewest terms while maintaining rich and complex dynamical behaviors comparable to the existing systems. Experimental observations are carried out via PSpice-based circuit simulations to validate the numerical simulation results.

This paper presents and analyzes a new four-dimensional (4D) jounce hysteresis chaotic dynamical system and investigates its application to robust communication. An adaptive chaotic synchronization scheme is developed based on the proposed 4D jounce system, in which an adaptive controller is designed at the receiver to achieve robust synchronization between the master and slave systems in the presence of uncertain system parameters. Lyapunov stability theory is employed to derive the adaptive control laws and parameter-update rules required for online estimation of the uncertain receiver-side parameters. For chaos-based communication, multiple information signals are encoded by modulating selected parameters of the chaotic transmitter system. At the receiver, the adaptive parameter estimator tracks the transmitted time-varying parameter, enabling reliable information recovery through a midpoint-thresholding decision scheme after the initial transient period. The performance and robustness of the proposed communication framework are evaluated through comprehensive numerical simulations under additive white Gaussian noise (AWGN) at different noise levels. The results demonstrate accurate chaotic synchronization, reliable information recovery, and robustness against channel noise, indicating the potential of the proposed 4D jounce chaotic system for robust and noise-tolerant communication applications.

Extreme events (EEs) in chaotic dynamics are rare broad excursions whose forecastability can be altered by dynamical noise. We investigate how noise changes EE occurrence and prediction skill across forecast horizons in a third-order autonomous chaotic flow. A single clean-data threshold is frozen for all realizations, broad events are defined by one maximum per excursion, and a future window W=15 is predicted from a 15-time-unit history using HistGradientBoosting with chronological data separation. As the forecast gap G between the observed history and the future event window increases, the clean Matthews correlation coefficient (MCC) decreases from 0.641 at G=0 to 0.165 at G=15. Noise dependence is evaluated with ten paired realizations at eight amplitudes. The mean short-horizon score increases from 0.456 in clean data to 0.546 at σ=0.007; the paired gain is 0.0895 (95% CI 0.0494–0.1295; Holm-adjusted p=0.0234). Noise strongly increases EE occurrence while event amplitude and width remain comparatively stable. Equalizing positive training counts across noise levels substantially attenuates the short-horizon gain, whereas strong noise reduces intermediate-horizon skill. We term this horizon-dependent, nonuniform change in forecast skill noise-induced predictability redistribution (NIPR).

The processing and transmission of information in a biological brain is assured by the neurons, which communicate together or process information through the emission of electrical impulses (called action potential). For this reason, a potential difference occurs both between neurons and between the inner and outer membranes of an individual neuron. Due to this, the biological neural network is constantly subjected to intricate electromagnetic conditions. In this study, a non-polynomial memristor is employed to simulate the impact of electromagnetic radiation on an improved Rulkov neuron. From the theoretical investigations carried out, the system shows both stable and unstable dynamics depending on the value of one of its specific parameters. Results from numerical analyses uncover that the improved Rulkov neuron under electromagnetic radiation can exhibit rich and diversified dynamics such as self-excited and hidden attractors, evolving from regular to chaotic motions. In addition, for certain specific values of its parameters, interesting and intriguing features such as antimonotonicity (i.e. bubble like bifurcation) and offset boosting are revealed. Furthermore, physical results obtained from breadboard experiments carried out using an Arduino Due microcontroller board corroborates with numerically obtained findings. The improved Rulkov neuron is finally exploited to generate random bits and NIST test is performed to confirm the unpredictable features of the generated bits.

Lung cancer is the deadliest cause of cancer-related deaths worldwide, and early and accurate detection is key to improving patient outcomes. IQ-OTH/NCCD CT scan images are used in this study to present an optimized computer-aided diagnosis (CAD) framework for lung cancer detection. In order to extract deep features and improve diagnostic accuracy, a weighted geometric mean (WGM) ensemble of pretrained convolutional neural networks (CNNs) called the LCD-VRD model—comprising VGG16, ResNet50V2, and DenseNet121—provides robust feature extraction and strong generalization capabilities for accurately classifying normal, benign, and malignant (cancerous) cases. To actively mitigate data imbalance and reduce model overfitting, real-time data augmentation alongside rigorous class weighting was implemented. The results show that, with 97.27% accuracy and a 97.24% F1-score, the WGM ensemble of these models performs exceptionally well. Furthermore, Gradient-weighted Class Activation Mapping (Grad-CAM) visualization was investigated on CT images to provide an exploratory qualitative visualization of the image regions associated with model predictions. While the proposed framework shows promise as an effective tool for automated lung cancer diagnosis, its validation is currently limited to the IQ-OTH/NCCD dataset. External dataset evaluation will be essential to fully establish robustness and clinical applicability.

The growing need to safeguard sensitive data in various fields, including in relation to education, banking over the phone, private voice conferences, and the military, has grown as dependence on technology in daily life has increased. Encryption schemes based on chaotic systems are among the most commonly utilized approaches in the security field due to their high levels of safety and reliability. This study proposes a secure audio encryption framework based on the Chameleon chaotic algorithm implemented on a Xilinx ZedBoard Zynq-7000 FPGA. The system was designed using a fixed-point arithmetic format with 32-bit precision (eight integers; 24 fractional bits) with the Xilinx System Generator in MATLAB Simulink R2021b and verified using Vivado. The Chameleon Chaotic System, characterized by its transition from self-excited to hidden attractors through parameter variation, adds complexity to the system dynamics and strengthens the encryption algorithm. The Adaptive Feedback Control technique was applied to synchronize the signals. These methods enhance the security of audio data by ensuring robust and fast synchronization during transmission. The performance of the proposed system was assessed using correlation analysis, the mean squared error, histogram analysis, and audio spectrogram analysis. The system demonstrated strong encryption capabilities with low correlation values (−0.0033). In decryption, they achieved high fidelity with a correlation exceeding 0.999 in noise-free conditions and above 0.9933 under 20 dB AWGN. Adaptive Feedback Control showed superior decryption precision with lower MSEU and higher PSNR, confirming its effectiveness under noisy environments.