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4 articles for “Hopf bifurcation”
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Hopf Bifurcation–Driven Chiral Amplification in an Oregonator-Based Oscillatory Chemical System with Optimal Control of Time-Scale Separation
Abstract: Nonlinear chemical systems exhibiting oscillatory kinetics and symmetry-breaking behavior have been widely studied in the context of reaction–diffusion chemistry and crystallization processes. However, the interaction between oscillatory dynamics and chiral amplification mechanisms remains insufficiently understood within a unified dynamical systems framework. This work aims to develop and analyze a reduced-order nonlinear model that couples an Oregonator-type activator–inhibitor system with a chiral response variable, and to investigate the role of Hopf …
Published in Journal of Control & Instrumentation · Vol. 17, Issue 3, 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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A Particle-Derived Nonlinear Dynamical Framework for Bubble Oscillations: Reduced-Order Modeling, Bifurcation Analysis, and Optimal Stabilization
Abstract: Particle-based fluid simulation has emerged as a powerful computational framework for modeling complex multiphase flows involving large deformations, moving interfaces, and nonlinear fluid interactions that challenge conventional mesh-based approaches. In this work, a nonlinear dynamical systems framework is developed for particle-resolved bubble oscillations by constructing a reduced-order model that preserves the dominant physical mechanisms governing bubble interface evolution. The formulation represents the bubble dynamics through coupled radial and shape deformation …
Published in Recent Trends in Fluid Mechanics · Vol. 13, Issue 2, 2026 · pp. 11–33 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