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7 articles for “Nonlinear oscillations”
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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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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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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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Self-similarities in Hilbert Envelope Energy Regions on Motion Waveforms Application in Detecting Motion Irregularities in Video Frames
Abstract: This paper introduces self-similar Hilbert envelope energy regions that are commonly found in oscillating spectral curves. The time-varying amplitudes and peak value frequencies in typical spectral curves reflect the response of a system to external stimuli. A Hilbert envelope is a smooth curve connected between spectral curve peak values. Each peak value on an envelope curve at time identifies an envelope-bounded region with interior area (called Hilbert envelope energy region …
Published in Trends in Opto-electro & Optical Communication · Vol. 14, Issue 3, 2024 · pp. 34–49 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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A Method of Mesh Deformation for Flow Analysis Around Oscillating Bodies
Abstract: In general, high-speed rotating machines are subjected to complex phenomena due to various reasons, such as increased noise and strong vibration due to dynamic unbalance, which affect the dynamic motion of rotating machines and are necessarily a problem to overcome. Therefore, it is necessary to have a mathematical model to simulate it, and a strong tool to solve the constructed model. Using fluid-structure coupling techniques, which are currently a powerful …
Published in Journal of Experimental & Applied Mechanics · Vol. 16, Issue 2, 2025 · pp. 35–42 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