Physica D: Nonlinear Phenomena最新文献_第2页

A novel underwater weak signal detection method based on High-order double-coupled duffing oscillator, Empirical wavelet transform and Hilbert transform 一种基于高阶双耦合duffing振荡器、经验小波变换和希尔伯特变换的水下微弱信号检测方法

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-30 DOI: 10.1016/j.physd.2025.134775

Yupeng Shen , Zhe Chen , Yaan Li , Weijia Li

{"title":"A novel underwater weak signal detection method based on High-order double-coupled duffing oscillator, Empirical wavelet transform and Hilbert transform","authors":"Yupeng Shen , Zhe Chen , Yaan Li , Weijia Li","doi":"10.1016/j.physd.2025.134775","DOIUrl":"10.1016/j.physd.2025.134775","url":null,"abstract":"<div><div>The increasing complexity of marine noise environments and advancements in stealth technology have significantly weakened the continuous spectrum of underwater signals, rendering traditional random signal analysis methods inadequate for weak signal detection amidst complex noise backgrounds. To address the challenge of detecting underwater weak signals at ultra-low Signal-to-Noise Ratios (SNR), we propose a novel detection method that integrates high-order double-coupled Duffing oscillator, Empirical Wavelet Transform (EWT), and Hilbert Transform. This approach begins with the introduction of a novel high-order double-coupled Duffing oscillator, whose dynamic behavior is thoroughly analyzed using nonlinear techniques, including Lyapunov exponents, bifurcation analysis, and entropy measures. The analysis proves that the improved Duffing oscillator has excellent robustness to different noise. Then, combined with the constructed geometric frequency array and the scale transformation, a new weak signal detection array that can detect any frequency is constructed. The system discerns the presence of underwater signals by monitoring changes in the attractor trajectory, specifically transitions from chaotic behavior to large-period or intermittent chaos. Finally, a novel frequency extraction method that leverages EWT and Hilbert Transform is proposed, which can achieve noise reduction and kurtosis optimization for intermittent chaotic signals, thereby extracting the actual frequency of underwater weak signals. Experimental results confirm that the proposed detection array effectively identifies underwater weak signals submerged in complex noise environments, achieving a detection SNR of -38.42 dB and an extracted signal frequency error of <1 %. The simulation results meet the stringent accuracy requirements for underwater sonar applications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134775"},"PeriodicalIF":2.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Nonlinear stability and instability of plasma boundary layers 等离子体边界层的非线性稳定性和不稳定性

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-30 DOI: 10.1016/j.physd.2025.134743

Masahiro Suzuki , Masahiro Takayama , Katherine Zhiyuan Zhang

引用次数: 0

Internal solitary and cnoidal waves of moderate amplitude in a two-layer fluid: the extended KdV equation approximation 两层流体中中等振幅的内孤立波和余弦波：扩展的KdV方程近似

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134723

Nerijus Sidorovas , Dmitri Tseluiko , Wooyoung Choi , Karima Khusnutdinova

引用次数: 0

On a class of exact solutions of the Ishimori equation 石森方程的一类精确解

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134746

Rustem N. Garifullin, Ismagil T. Habibullin

引用次数: 0

Steady compressible 3D Euler flows in toroidal volumes without continuous Euclidean isometries 无连续欧几里德等距的稳定可压缩三维欧拉流环面体

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134741

Naoki Sato , Michio Yamada

引用次数: 0

Direct linearisation of the non-commutative Kadomtsev–Petviashvili equations 非交换Kadomtsev-Petviashvili方程的直接线性化

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134745

Gordon Blower , Simon J.A. Malham

{"title":"Direct linearisation of the non-commutative Kadomtsev–Petviashvili equations","authors":"Gordon Blower , Simon J.A. Malham","doi":"10.1016/j.physd.2025.134745","DOIUrl":"10.1016/j.physd.2025.134745","url":null,"abstract":"<div><div>We prove that the non-commutative Kadomtsev–Petviashvili (KP) equation and a ‘lifted’ modified Kadomtsev–Petviashvili (mKP) equation are directly linearisable, and thus integrable in this sense. There are several versions of the non-commutative mKP equations, including the two-dimensional generalisations of the non-commutative modified Korteweg–de Vries (mKdV) equation and its alternative form (amKdV). Herein we derive the ‘lifted’ mKP equation, whose solutions are the natural two-dimensional extension of those for the non-commutative mKdV equation derived in Blower and Malham (2023). We also present the log-potential form of the mKP equation, from which all of these non-commutative mKP equations can be derived. To achieve the integrability results, we construct the pre-Pöppe algebra that underlies the KP and mKP equations. This is a non-commutative polynomial algebra over the real line generated by the solution (and its partial derivatives) to the linearised form of the KP and mKP equations. The algebra is endowed with a pre-Pöppe product, based on the product rule for semi-additive operators pioneered by Pöppe for the commutative KP equation. Integrability corresponds to establishing a particular polynomial expansion in the respective pre-Pöppe algebra. We also present numerical simulations of soliton-like interactions for the non-commutative KP equation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134745"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Pulse solutions in Gierer–Meinhardt equation with slowly degenerate nonlinearity 慢退化非线性Gierer-Meinhardt方程的脉冲解

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134738

Yuanxian Chen , Jianhe Shen

{"title":"Pulse solutions in Gierer–Meinhardt equation with slowly degenerate nonlinearity","authors":"Yuanxian Chen , Jianhe Shen","doi":"10.1016/j.physd.2025.134738","DOIUrl":"10.1016/j.physd.2025.134738","url":null,"abstract":"<div><div>Based on geometric singular perturbation theory (GSPT) and nonlocal eigenvalue problem (NLEP) method, this article studies the existence and stability of algebraically delaying pulses in Gierer–Meinhardt equation with slowly degenerate nonlinearity. By utilizing the fact that the critical manifold is both normally hyperbolic and invariant, we rigorously establish the existence of algebraically decaying pulses by combining GSPT with the Melnikov method. It is proven that the model has a unique algebraically decaying pulse. On the other hand, the slowly degenerate nonlinearity results in that the linearized matrix associated with the eigenvalue problem no longer approaches the constant matrix exponentially. Hence, we must solve the resulting linear “time-varying” problem. By classifying the power of the slowly degenerate nonlinearity, we introduce different special functions including the Whittaker function and the Bessel function to solve this linear problem explicitly. Thus the spectral (in)stability criteria on the algebraically delaying pulse can be set up by matching the slow and fast segments of the eigenfunctions. An example is also provided to illustrate the theoretical framework.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"481 ","pages":"Article 134738"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144205650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

On the local structure of degenerate Teixeira singularities in 3D Filippov systems 三维Filippov系统退化Teixeira奇点的局部结构

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134735

Oscar A.R. Cespedes , Rony Cristiano , Otávio M.L. Gomide

{"title":"On the local structure of degenerate Teixeira singularities in 3D Filippov systems","authors":"Oscar A.R. Cespedes , Rony Cristiano , Otávio M.L. Gomide","doi":"10.1016/j.physd.2025.134735","DOIUrl":"10.1016/j.physd.2025.134735","url":null,"abstract":"<div><div>The main goal of this paper is to emphasize the richness of the dynamics emanating from degeneracies at the so-called T-singularity in <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> Filippov systems. More specifically, we characterize the local sliding and crossing dynamics around an invisible two-fold singularity in <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> Filippov systems which presents a degeneracy arising from the contact between the tangency fold curves of a system with the switching manifold. In particular, we prove that, when the contact between such curves is 2 or 3 at this point, then it presents a nonsmooth diabolo emanating from it which has one branch or two branches, respectively.</div><div>We also analyze global bifurcations of a family of Filippov systems which presents an invisible two-fold singularity having a cubic contact between the fold curves and we show that there is an invariant surface foliated by crossing heteroclinic orbits between <span><math><mi>T</mi></math></span>-singularities bifurcating from this degenerate singularity. Finally, we show that such kind of scenario appears naturally in applied models of switched electronic circuits and this singularity is realized in an specific model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"480 ","pages":"Article 134735"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144185097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Revisiting amplitude death in the presence of diffusion asymmetry 在扩散不对称的情况下重新审视振幅死亡

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134740

Garima Saxena

引用次数: 0

Shielding of breathers for the focusing nonlinear Schrödinger equation 聚焦非线性Schrödinger方程的呼吸器屏蔽

IF 2.7 3区数学

Physica D: Nonlinear Phenomena Pub Date : 2025-05-29 DOI: 10.1016/j.physd.2025.134744

Gregorio Falqui , Tamara Grava , Christian Puntini

引用次数: 0