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58 articles for “nonlinear dynamics”
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Symmetry Breaking in Mathematical Models: Bifurcation, Chaos, and Pattern Formation
Abstract: Symmetry breaking serves as a central organizing principle in the understanding of nonlinear systems across physics, biology, chemistry, and engineering. When a system transitions from a symmetric state to an asymmetric configuration, it often signals the onset of new structures, dynamic behaviors, or even chaotic regimes. This review explores symmetry breaking from the theoretical and mathematical perspectives of bifurcation theory, chaos theory, and pattern formation. We discuss how small parameter …
Published in Emerging Trends in Symmetry · Vol. 1, Issue 2, 2025 · pp. 25–30 Read article
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Role of Prey Refuge in Predator-Prey Dynamics with Nonlinear Functional Responses: A Mathematical Approach
Abstract: The Beddington-DeAnglis and Holling type II functional response with prey refuge are used in this study to propose and assess a prey-predator system. This study looks at the ecological effects of prey refuge and how it affects predator-prey relationships, highlighting how functional responses influence population dynamics. The dynamical behavior of the model has been shown, which consist the existence of positivity, boundedness, local stability, and global stability. In addition, stability …
Published in Journal of Polymer & Composites · Vol. 13, Issue 3, 2025 · pp. 523–537 Read article
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“Microvita‑Inspired Informational Field Dynamics as a Nonlinear Signal‑Generation Mechanism in Matter–Life–Mind Systems”
Abstract: Recognizing how matter, life, and consciousness relate to one another continues to be among the most essential challenges faced by modern science. Contemporary physical theories successfully describe the behavior of elementary particles and large-scale cosmological structures, yet they do not fully explain the emergence of informational complexity and organized patterns observed in biological and cognitive systems. This study proposes a theoretical framework in which Microvita are interpreted as subtle informational …
Published in Current Trends in Signal Processing · Vol. 16, Issue 1, 2026 Read article
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Key Generation Algorithms Using Difference Equations with Multi-Precision Arithmetic: A Review
Abstract: Modern cryptographic systems rely on robust key generation to secure data and communication. This review explores the integration of difference equations and multi-precision arithmetic for cryptographic key generation, addressing limitations in traditional methods like pseudorandom number generators and chaotic systems. Difference equations produce deterministic yet chaotic sequences ideal for cryptography due to their sensitivity to initial conditions and nonlinearity. However, finite precision arithmetic can lead to periodicity and loss of …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 3, 2024 · pp. 23–36 Read article
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Adaptive Robust Constraint-Based Nonlinear Control for Trajectory Tracking and Dynamic Obstacle Avoidance in Multi-copter UAVs
Abstract: An adaptive robust nonlinear control system for multi-copter unmanned aerial vehicles (UAVs) trajectory tracking and obstacle avoidance is presented in this research. The suggested approach addresses nonlinear dynamics and environmental uncertainties by combining adaptive disturbance estimates with constraint-based control. Nonlinear differential equations are used to simulate the motion of the UAV, with obstacle avoidance represented as an inequality constraint and trajectory tracking as an equality constraint. The Udwadia–Kalaba method is …
Published in International Journal on Drones · Vol. 2, Issue 2, 2026 · pp. 01–08 Read article
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Lyapunov-Stable Adaptive Fractional-Order Interval Type-2 Fuzzy Control for Robust Anti-Lock Braking Under Uncertain Road Adhesion Conditions
Abstract: This paper proposes a Lyapunov-stable Adaptive Fractional-Order Interval Type-2 Fuzzy Logic Controller (FO-IT2FLC) for robust anti-lock braking system (ABS) control under nonlinear vehicle dynamics and uncertain road adhesion conditions. The proposed framework integrates fractional-order error dynamics to capture memory-dependent tire–road interaction, interval Type-2 fuzzy inference to model uncertainty via footprint-of-uncertainty representation, and a Lyapunov-based adaptive learning mechanism for real-time parameter tuning. A rigorous stability proof guarantees boundedness of all closed-loop …
Published in Journal of Control & Instrumentation · Vol. 17, Issue 2, 2026 Read article
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Artificial Intelligence–Assisted Reduced-Order Modeling and Stability Control in Granular Couette Flow
Abstract: This study develops a reduced-order and stability-aware modeling framework for dense granular Couette flow by integrating continuum mechanics, bifurcation analysis, and data-driven stability estimation. Starting from coupled governing equations for momentum, granular temperature, and microstructural evolution, the system is nondimensionalized and reduced using a Galerkin projection consistent with shear-driven boundary conditions. This yields a low-dimensional nonlinear dynamical system that preserves the essential coupling between velocity, fluctuation energy, and structural relaxation. …
Published in Emerging Trends in Chemical Engineering · Vol. 13, Issue 3, 2026 Read article
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First Order Sliding Mode Control of Coupled Tank System
Abstract: This paper investigates the challenging problem of liquid level control in Coupled Tank Systems (CTS). CTS, characterized by its nonlinear behaviour and sensitivity to disturbances, presents significant control challenges. This report suggests and assesses several control measures to solve these problems. Mathematical models are developed to capture the system's nonlinear dynamics, and controllers such as Proportional-Integral (PI) and Sliding Mode Controllers (SMC) are designed. The PI controller effectively regulates the …
Published in Trends in Electrical Engineering · Vol. 14, Issue 3, 2024 Read article
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Spatiotemporal Analysis of Mean-Field Coupled Lorenz Oscillators for Applications in Electronic Network Design and Chaotic Synchronization
Abstract: This study investigates the spatiotemporal behavior of a network of 100 coupled Lorenz oscillators interacting through mean-field coupling with coupling strength κ = 0.1 and explores its relevance to electronic system design and nonlinear network architectures. While each oscillator follows classical Lorenz dynamics, the coupling mechanism enables collective behavior that resembles synchronization phenomena observed in distributed electronic and communication systems. Numerical simulations reveal rich dynamical characteristics including partial synchronization, emergent …
Published in Journal of Electronic Design Technology · Vol. 17, Issue 2, 2026 Read article
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ANN-Based Adaptive Rotor Current Control for DFIG Wind Systems: A Comparative Dynamic Analysis
Abstract: The variability of rotor current management in Doubly Fed Induction Generator (DFIG)-based wind energy conversion systems is crucial for maintaining stability in power extraction under fluctuating wind and grid circumstances. Traditional proportional-integral (PI) controllers, despite their ease of use, frequently exhibit diminished performance when faced with parameter uncertainty, nonlinear behaviors, and rapid wind fluctuations.This paper presents an adaptive rotor current control strategy, which is an Artificial Neural Network (ANN)-based approach …
Published in Journal of Power Electronics and Power Systems · Vol. 16, Issue 1, 2026 · pp. 41–53 Read article
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Static and Dynamic Analysis of Conventional, Diagrid and Hexagrid Systems Across Different Storey Heights
Abstract: In structural engineering, multi-storey buildings’ seismic resilience in earthquake-prone areas is crucial. The seismic performance of proposed multi-story buildings with different heights (G+13, G+19, and G+27) is thoroughly examined in this study using traditional structural systems that are octagrid and hexagrid. Under seismic zone III conditions, the study evaluates important parameters such as storey drifts and storey displacements using the Response Spectrum Method. Each structural system's seismic response is assessed …
Published in Journal of Offshore Structure and Technology · Vol. 12, Issue 2, 2025 · pp. 36–47 Read article
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Noise-Driven Collective Behavior in Mean-Field Coupled Lorenz Oscillator Networks
Abstract: This work investigates the spatiotemporal dynamics of an ensemble of 100 identical Lorenz oscillators coupled through a mean-field scheme in the presence of additive noise. Building on prior studies of spatiotemporal chaos in coupled Lorenz arrays and mean-field coupled chaotic oscillators, the focus is on how the competition between deterministic coupling and stochastic forcing shapes collective behavior, including complete synchronization, desynchronization, clustered states, and noise-modified spatiotemporal chaos. The governing equations …
Published in International Journal of Advanced Control and System Engineering · Vol. 4, Issue 2, 2026 Read article
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From Differential Equations to Data Science: A Survey on Analytical Methods in Contemporary Problems
Abstract: The integration of differential equations and data science methods represents a dynamic and evolving approach to solving contemporary challenges across a wide range of disciplines, including engineering, physics, biology, economics, and finance. Differential equations have long served as fundamental tools for modeling continuous systems and processes, offering powerful insights into the behavior of natural and man-made phenomena. For example, they describe how heat diffuses through materials, how populations grow in …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 1–6 Read article
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Seismic Analysis of Conventional, Hexagrid and Octagrid Steel Structural Systems
Abstract: The seismic resilience of multi-story buildings in earthquake-prone regions is a critical consideration in structural engineering. This dissertation presents a comprehensive analysis of the seismic performance of proposed multi-story buildings with varying heights (G+10, G+15, and G+20) using conventional, hexagrid, and octagrid structural systems. The study utilizes the Response Spectrum Method under seismic zone Ⅴ conditions to assess key parameters including storey drift, storey displacement, base shear, and overturning moment. …
Published in Journal of Structural Engineering and Management · Vol. 11, Issue 1, 2024 · pp. 26–41 Read article
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(𝛅,Ü ) Convex Structure on Partial B-Metric Space Concerning Quasi Contraction and Fixed-Point Results
Abstract: This work introduces the concept of (δ,Ü )– Convex Partial b-Metric Spaces using convex structure. Motivated by this approach, we demonstrated fixed point results and their uniqueness, as well as quasi contraction, and provided some supporting instances for the established results. Our findings expand prior fixed-point results to a novel concept (δ,Ü )– Convex Partial b-Metric Spaces. To support our theoretical findings, we provide several instances that exemplify the established …
Published in Recent Trends in Mathematics · Vol. 1, Issue 1, 2024 Read article
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Advanced Control Techniques: Super-twisting Controller Applications and Insights
Abstract: Sliding mode control (SMC) provides robust control for uncertain systems. This study focuses on the Super-Twisting Controller (STC), a powerful SMC technique known for its finite-time convergence and robustness. Its importance is to provide chatter-free control and robustness against uncertainty, and make it suitable for systems with nonlinear dynamics and disturbances. The advantages of STC are faster speed, more accurate control actions, and enhanced system stability, though may require careful …
Published in Journal of Experimental & Applied Mechanics · Vol. 15, Issue 2, 2024 · pp. 1–7 Read article
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AI-Assisted Gain Scheduling for Real-Time Temperature Control in Chemical Reactors
Abstract: Temperature control in continuous stirred-tank reactors (CSTR) represents a critical challenge in chemical process industries due to inherent nonlinearities, time-varying dynamics, and parametric uncertainties. Conventional proportional-integral-derivative (PID) controllers with fixed gains often fail to maintain optimal performance across varying operating conditions, leading to temperature excursions that compromise product quality and safety. This paper presents a novel AI-assisted gain scheduling framework that integrates artificial neural networks (ANN) with adaptive PID control …
Published in Journal of Control & Instrumentation · Vol. 17, Issue 1, 2026 · pp. 24–33 Read article
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Mathematical Approaches to Nonlinear Oscillatory Systems with Damping: Exact and Approximate Solutions
Abstract: The study of nonlinear oscillatory systems with damping is a key area of research in applied mathematics, particularly in the context of dynamical systems, stability analysis, and bifurcation theory. These systems, described by second-order nonlinear differential equations, exhibit a rich variety of behaviors, including periodic, quasi-periodic, and chaotic motions. The introduction of damping—representing energy dissipation—adds a layer of complexity, making the analytical and numerical solution of such systems a challenging …
Published in Recent Trends in Mathematics · Vol. 2, Issue 2, 2025 · pp. 7–11 Read article
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Study on Single-Slope Solar Still for Experimental and Data-Driven Analysis for Improving Productivity with Different Basin Materials.
Abstract: This study investigates the single-slope solar still under the diurnal variation of water temperature and distillate yield under identical operating conditions. Experimental analysis was conducted to evaluate the performance enhancement through the incorporation of natural basin materials, namely hemp and sand. The water distillation process is focused on improving potable water productivity and thermal behaviour. The inclusion of hemp and sand in the basin leads to noticeable differences in productivity …
Published in Emerging Trends in Chemical Engineering · Vol. 13, Issue 2, 2026 · pp. 31–46 Read article
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A Novel Mathematical Exploration of Fractal Dynamics in Hyperbolic Spaces
Abstract: This research paper presents an original study on the behavior, generation, and properties of fractal structures within hyperbolic geometry. Unlike classical Euclidean fractals, hyperbolic fractals demonstrate accelerated boundary complexity and distinct scaling symmetries due to the curvature of the underlying space. The paper proposes new iterative models, analyzes geometric invariants, and explores potential applications in data visualization, network science, and theoretical physics. This research paper conducts an in-depth investigation into …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 1–7 Read article