IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0346786

Daniel Frühwald, Christopher Odefey, Thomas Lilienkamp

引用次数: 0

A numerical study on the dynamics of non-inertial and inertial particles in geophysical flows. 地球物理流动中非惯性和惯性粒子动力学的数值研究。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0323103

Nishanta Baral, Eric Forgoston, M Ani Hsieh

{"title":"A numerical study on the dynamics of non-inertial and inertial particles in geophysical flows.","authors":"Nishanta Baral, Eric Forgoston, M Ani Hsieh","doi":"10.1063/5.0323103","DOIUrl":"https://doi.org/10.1063/5.0323103","url":null,"abstract":"We consider the dynamics of non-inertial and inertial particles in several types of geophysical flows. The underlying structures of the flow fields are examined via their associated Lagrangian coherent structures, which are found by computing the finite-time Lyapunov exponent (FTLE) field. For inertial particles with finite size and mass, the Maxey-Riley equation is used to describe the particles' motion and to find the inertial FTLE field. We compare the behavior and FTLE fields of massless non-inertial particles and light (bubbles) and heavy (aerosols) inertial particles using the velocity fields from the double-gyre flow, Bickley jet, and eddy-quadrupole models, as well as an ocean dataset of Monterey Bay, California. In addition, we explore the preferential aggregation of inertial particles in these flows and show that inertia affects particle transport: aerosols accumulate along maximal FTLE ridges, and bubbles cluster inside vortex cores, where the clustering depends on the density ratio and the Stokes number. Inclusion of the Coriolis force further influences the dynamics via ejection of particles between cyclonic and anticyclonic structures, where the rate of aggregation onto these rotational attractors increases with the strength of rotation. We also study the validity of ignoring the Faxén correction and an often used assumption whereby the material derivative is set equal to the total derivative. The Faxén correction has a negligible effect for these flows, while the material derivative simplification changes the timescale on which inertial particles aggregate onto their attractors.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148918315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Phase space reorganization and traveling wave emergence driven by non-Kerr effects in nonparaxial optical media. 非近轴光学介质中非克尔效应驱动的相空间重组和行波出现。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0343336

Naresh Saha, Nirmoy Kumar Das, Ashoke Das, Arnob Ray

{"title":"Phase space reorganization and traveling wave emergence driven by non-Kerr effects in nonparaxial optical media.","authors":"Naresh Saha, Nirmoy Kumar Das, Ashoke Das, Arnob Ray","doi":"10.1063/5.0343336","DOIUrl":"https://doi.org/10.1063/5.0343336","url":null,"abstract":"In this article, the nonlinear Helmholtz equation with non-Kerr nonlinearity, such as self-steepening and self-frequency shift, is considered. A traveling wave transformation is applied, and an extended nonlinear Helmholtz equation is reduced to a Hamiltonian dynamical system. Then, the reduced Hamiltonian system is analyzed by the classification of equilibrium points, phase space analysis, and the construction of exact wave solutions. The relationship between the reduced dynamical coefficients and the original physical parameters is further established through a parameter space analysis. It is shown that self-steepening directly modifies the reduced dynamics, whereas self-frequency shift acts through the compatibility condition for the real traveling wave reduction. Together, these non-Kerr effects reshape the phase space geometry and traveling wave structure. Localized and periodic traveling waves are obtained, with their existence determined by the balance among dispersion, nonparaxiality, Kerr nonlinearity, and non-Kerr effects. Furthermore, a periodically forced version of the reduced system is examined to study the transition from regular to irregular dynamics. It has been observed that external forcing can induce complex oscillatory behavior. Bifurcation analysis, time series evolution, phase space, largest Lyapunov exponent, and Poincaré section demonstrate the emergence of quasiperiodic and chaotic responses under sufficiently strong forcing. All analytical branches are verified through full-equation residual evaluation, while few selected branches are additionally examined through direct numerical propagation and robustness tests under complex Gaussian perturbations. The results show that self-steepening directly renormalizes the effective nonlinear dynamics, whereas self-frequency shift restricts the admissible real-envelope traveling wave manifold.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148873253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Organized structures and multiple attractors in chaotic regimes. 混沌状态下的有组织结构和多吸引子。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0346275

Purbasha Deb, G C Layek

{"title":"Organized structures and multiple attractors in chaotic regimes.","authors":"Purbasha Deb, G C Layek","doi":"10.1063/5.0346275","DOIUrl":"https://doi.org/10.1063/5.0346275","url":null,"abstract":"Deterministic chaotic systems often exhibit highly organized structures in both phase space and parameter space. In this work, we investigate two-dimensional Hénon-like extensions of the discrete Gaussian and cubic maps incorporating a linear feedback channel. The Gaussian-based model admits a natural realization as a nonlinear electronic circuit consisting of a Gaussian-saturating amplifier coupled to a linear memory feedback loop. A detailed bifurcation analysis reveals that, while the classical one-dimensional Gaussian map is primarily organized by fold and flip bifurcations together with period-bubbling routes to chaos, its two-dimensional extension possesses a substantially richer dynamical structure. In particular, the system exhibits Neimark-Sacker bifurcations, quasiperiodic dynamics, Arnold tongues generated through frequency locking, shrimp-shaped periodic stability regions embedded within chaotic regimes, and extensive multistability. The observed Arnold tongues follow the classical Farey-tree hierarchy of rotation numbers and organize the resonance structure of the parameter space. Furthermore, coexistence of attractors is demonstrated through bistability between period-9 and period-14 oscillations for identical parameter values. The corresponding basins of attraction display strong intermingling, and the computed basin entropy (Sb = 0.6032) indicates fractal basin boundaries and pronounced sensitivity to initial conditions. In addition, although the one-dimensional cubic map already exhibits shrimp-shaped periodic windows, its two-dimensional extension reveals nested shrimp families together with resonance tongue structures, substantially enriching the global bifurcation landscape. These results show that low-dimensional nonlinear maps can generate highly organized parameter-space architectures in which periodic, quasiperiodic, and chaotic dynamics coexist through well-defined bifurcation mechanisms.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148905120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized PT-symmetric nonlinear Dirac equation: Exact solitary waves solutions, stability, and conservation laws. 广义pt对称非线性狄拉克方程：精确孤波解，稳定性和守恒定律。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0336442

Fernando Carreño-Navas, Siannah Peñaranda, Renato Alvarez-Nodarse, Niurka R Quintero

引用次数: 0

Cluster dynamics in a two-group Stuart-Landau model analyzed by the second-order phase reduction. 用二阶相约简分析两群Stuart-Landau模型中的聚类动力学。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0346282

Yernur Baibolatov, Oleh E Omel'chenko, Michael Rosenblum

引用次数: 0

Hierarchical frequency-locking organization and quint points in a periodically driven FitzHugh-Nagumo neuron model. 周期驱动FitzHugh-Nagumo神经元模型的层次锁频组织和int点。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0330457

Nivea D Bosco, Fabio S Ramos, Marcus W Beims, Cesar Manchein

引用次数: 0

Permutation entropy reveals coherent structures and ecological boundaries in North Atlantic phytoplankton blooms. 排列熵揭示了北大西洋浮游植物华的连贯结构和生态边界。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0336325

Giulio Tirabassi, Daniele Iudicone, Enrico Ser-Giacomi

{"title":"Permutation entropy reveals coherent structures and ecological boundaries in North Atlantic phytoplankton blooms.","authors":"Giulio Tirabassi, Daniele Iudicone, Enrico Ser-Giacomi","doi":"10.1063/5.0336325","DOIUrl":"https://doi.org/10.1063/5.0336325","url":null,"abstract":"We apply ordinal-pattern analysis and permutation entropy (PE) to satellite-derived chlorophyll-a (Chl-a), sea surface temperature (SST), and mixed-layer depth (MLD) data to investigate the spatiotemporal dynamics of the North Atlantic phytoplankton spring bloom. Using both temporal and spatial versions of PE, together with mutual information-based functional networks, we identify coherent dynamical regimes and ecological boundaries that are difficult to detect with classical linear methods. Temporal PE at the annual time scale reveals two well-separated low-entropy regions corresponding to the North Atlantic Subtropical and Subpolar Gyres, divided by a sharp zonal boundary consistent with a transition between light-limited and nutrient-limited phytoplankton regimes. Area-Weighted Connectivity maps further suggest that the Subpolar bloom region is itself divided into two dynamically distinct subregions in the Labrador and Irminger Seas. Analysis of spatial PE uncovers a characteristic entropy-chlorophyll cycle in which bloom growth occurs during periods of high spatial disorder, while the recession phase is associated with the emergence of large-scale meridional Chl-a gradients. Mutual information between Chl-a and physical drivers reveals seasonal, predominantly non-linear coupling with SST and MLD, with SST exhibiting a significant negative correlation during spring and autumn and MLD showing surprisingly weak local control during the bloom phase. Our results demonstrate the potential of ordinal-pattern methods as a complementary, model-free framework for characterizing the interplay between ocean physics and marine ecosystem dynamics from remote sensing observations.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149015890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Erratum: "Differential impacts of grazing on vegetation patterning in drylands: A comparative study" [Chaos 35, 113126 (2025)]. 勘误：“放牧对旱地植被格局的差异影响：一个比较研究”[混沌35,113126(2025)]。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0353538

Kalyanashis Sahoo, Jayita Koley, Santu Ghorai, Swarup Poria

引用次数: 0

Chimera states, synchronization, and energy consumption in a chaotic electrically coupled Hindmarsh-Rose neural network under multiple memory effects. 多重记忆效应下混沌电耦合Hindmarsh-Rose神经网络的嵌合体状态、同步和能量消耗。

IF 3.3 2区数学

Chaos Pub Date : 2026-09-01 DOI: 10.1063/5.0336997

Armand Sylvin Etémé, Alain Mvogo, Saralees Nadarajah, Henri Paul Ekobena Fouda, Timoléon Crépin Kofané, Conrad Bertrand Tabi

{"title":"Chimera states, synchronization, and energy consumption in a chaotic electrically coupled Hindmarsh-Rose neural network under multiple memory effects.","authors":"Armand Sylvin Etémé, Alain Mvogo, Saralees Nadarajah, Henri Paul Ekobena Fouda, Timoléon Crépin Kofané, Conrad Bertrand Tabi","doi":"10.1063/5.0336997","DOIUrl":"https://doi.org/10.1063/5.0336997","url":null,"abstract":"We investigate memory-induced collective dynamics in a ring of electrically coupled Hindmarsh-Rose neurons operating in a chaotic bursting regime. The effects of long-range interactions, diffusion delay, reaction delay, and electromagnetic induction on spatiotemporal organization and Hamiltonian energy density are systematically analyzed. The dynamics is quantified using five complementary statistical indicators: the synchronization factor, the strength of incoherence, the discontinuity measure, the skewness measure, and the time-averaged Hamiltonian energy density. Depending on the memory parameters, the network exhibits asynchronous, chimera, multichimera, and synchronized states. We show that long-range interactions increase the Hamiltonian energy density and enhance the level of collective activity, although they predominantly generate asynchronous states when acting alone. Diffusion delay generates a rich variety of collective states, ranging from asynchronous and chimera patterns to complete synchronization depending on the interaction range, while reaction delay predominantly supports asynchronous, chimera, and multichimera dynamics. In contrast, electromagnetic induction promotes global synchronization from a critical memristive coupling threshold. Furthermore, the Hamiltonian energy density increases monotonically with the interaction range, reaction delay, and memristive feedback strength, whereas it exhibits a non-monotonic dependence on diffusion delay. These findings demonstrate that multiple memory mechanisms interact synergistically and competitively to shape neuronal coordination, energy localization, and pattern formation, providing new insights into the design of robust neuromorphic systems and brain-inspired algorithms.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"36 9","pages":""},"PeriodicalIF":3.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148873162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

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