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Beltrami fields and knotted vortex structures in incompressible fluid flows
Bulletin of the London Mathematical Society, Volume 55, Issue 3, Page 1059-1103, June 2023., 2023 Abstract This paper gives a survey on recent results about the existence of knotted vortex structures in incompressible fluids. This includes the proof of Lord Kelvin's conjecture on the existence of knotted vortex tubes in steady Euler flows and a new probabilistic approach to address Arnold's speculation that typical Beltrami fields should exhibit ...
Alberto Enciso, Daniel Peralta‐Salas
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Natural Exponential and Three‐Dimensional Chaotic System
Advanced Science, Volume 10, Issue 15, May 26, 2023., 2023 A novel natural exponential and three‐dimensional chaotic system with higher sensitivity to initial condition is presented. Its characterizations are revealed via various chaotic dynamic indicators. The performance evaluation through recursive and entropy study verifies the model complexity and robustness, while the feasibility of this system is ...
Shiwei Liu +4 more
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Arnold Diffusion, Quantitative Estimates, and Stochastic Behavior in the Three‐Body Problem
Communications on Pure and Applied Mathematics, Volume 76, Issue 3, Page 616-681, March 2023., 2023 Abstract We consider a class of autonomous Hamiltonian systems subject to small, time‐periodic perturbations. When the perturbation parameter is set to zero, the energy of the system is preserved. This is no longer the case when the perturbation parameter is non‐zero.
Maciej J. Capiński, Marian Gidea
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International Journal of Mechanical System Dynamics, Volume 3, Issue 1, Page 85-94, March 2023., 2023 Abstract Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems. In this paper, a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an example.
Yong Huang
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Symplectomorphisms with positive metric entropy
Proceedings of the London Mathematical Society, Volume 124, Issue 5, Page 691-712, May 2022., 2022 Abstract We obtain a dichotomy for C1$C^1$‐generic symplectomorphisms: either all the Lyapunov exponents of almost every point vanish, or the map is partially hyperbolic and ergodic with respect to volume. This completes a program first put forth by Ricardo Mañé. A key ingredient is an analysis of partially hyperbolic sets of positive volume.
Artur Avila +2 more
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Chaotic Threshold of a Nonlinear Zener Systems Based on the Melnikov Method
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Regarding a nonlinear Zener model with a viscoelastic Maxwell element as the research object, the complicated dynamic behaviors such as homoclinic bifurcation and chaos under harmonic excitation are investigated. At first, the analytically necessary condition for chaos in the sense of Smale horseshoe is derived based on the Melnikov method.
Shutong Fan +3 more
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High-Order Melnikov Method for Time-Periodic Equations
Advanced Nonlinear Studies, 2017 This paper discusses a high-order Melnikov method for periodically perturbed equations. We introduce a new method to compute Mk(t0){M_{k}(t_{0})} for all k≥0{k\geq 0}, among which M0(t0){M_{0}(t_{0})} is the traditional Melnikov function, and M1(t0 ...
Chen Fengjuan, Wang Qiudong
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Maxwell Fronts in the Discrete Nonlinear Schrödinger Equations With Competing Nonlinearities
Studies in Applied Mathematics, Volume 156, Issue 2, February 2026.ABSTRACT In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schrödinger (DNLS) equations are often employed to model these dynamics, particularly in the context of Bose–Einstein condensates and optical ...
Farrell Theodore Adriano, Hadi Susanto
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SECURITY AND PRIVACY, Volume 9, Issue 1, January/February 2026.ABSTRACT Unarguably, malware and their variants have metamorphosed into objects of attack and cyber warfare. These issues have directed research focus to modeling infrastructural settings and infection scenarios, analyzing propagation mechanisms, and conducting studies that highlight optimized remedial measures.
Chukwunonso Henry Nwokoye
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International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.This study examines the second‐order Kuramoto model within a specific small invariant subspace. We explore how the damping parameter influences the emergence of synchronized states and the weak chimera state in this model. In addition, we numerically investigate various behaviors in the phase space resulting from changes in the damping parameter and ...
Mary G. Thoubaan +4 more
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