Pub Date : 2026-02-06DOI: 10.1016/j.amc.2026.130007
Gabriel Rondón, Nasrin Sadri
{"title":"Global dynamics of generalized Duffing oscillators with global centers","authors":"Gabriel Rondón, Nasrin Sadri","doi":"10.1016/j.amc.2026.130007","DOIUrl":"https://doi.org/10.1016/j.amc.2026.130007","url":null,"abstract":"","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"46 1","pages":""},"PeriodicalIF":4.0,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134765","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}
Pub Date : 2026-02-06DOI: 10.1016/j.jde.2026.114187
Jie Guo, Quansen Jiu
In this paper, we study the generalized Proudman-Johnson equation posed on the torus. In the critical regime where the parameter a is close to and slightly greater than 1, we establish finite time blow-up of smooth solutions to the inviscid case. Moreover, we show that the blow-up is asymptotically self-similar for a class of smooth initial data. In contrast, when the parameter a lies slightly below 1, we prove the global in time existence for the same initial data. In addition, we demonstrate that inviscid Proudman-Johnson equation with Hölder continuous data also develops a self-similar blow-up. Finally, for the viscous case with , we prove that smooth initial data can still lead to finite time blow-up.
{"title":"Finite time blow-up analysis for the generalized Proudman-Johnson model","authors":"Jie Guo, Quansen Jiu","doi":"10.1016/j.jde.2026.114187","DOIUrl":"10.1016/j.jde.2026.114187","url":null,"abstract":"<div><div>In this paper, we study the generalized Proudman-Johnson equation posed on the torus. In the critical regime where the parameter <em>a</em> is close to and slightly greater than 1, we establish finite time blow-up of smooth solutions to the inviscid case. Moreover, we show that the blow-up is asymptotically self-similar for a class of smooth initial data. In contrast, when the parameter <em>a</em> lies slightly below 1, we prove the global in time existence for the same initial data. In addition, we demonstrate that inviscid Proudman-Johnson equation with Hölder continuous data also develops a self-similar blow-up. Finally, for the viscous case with <span><math><mi>a</mi><mo>></mo><mn>1</mn></math></span>, we prove that smooth initial data can still lead to finite time blow-up.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114187"},"PeriodicalIF":2.3,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122620","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}
Pub Date : 2026-02-06DOI: 10.1007/s00285-026-02350-0
Shih-Hsun Hung, Je-Chiang Tsai, Chih-Chi Wu
We investigate noise-induced bimodal distributions in self-regulated gene networks with fast dimerization, where dimerized proteins enhance gene expression. Despite their fundamental role in gene regulation, analytical study of bimodal behaviour in such networks is challenging because the nonlinear interactions introduced by dimer formation render exact steady-state distributions infeasible. To address this, we reformulate the problem as a reduced self-regulated gene-expression model that approximates fast dimerization, in which the transition rate from the promoter-off to promoter-on state depends nonlinearly on protein levels. We introduce two diagnostic quantities: the promoter activity ratio, which quantifies promoter activation as a function of protein level, and the mode detection ratio, which identifies peaks of the steady-state protein distribution. Analysis of their recurrence relations reveals how promoter activity shapes the steady-state law, and how intrinsic stochasticity can generate multimodal protein distributions in self-regulated expression circuits. We further show that the corresponding mean-field ODE system admits a unique non-negative equilibrium when the protein synthesis-to-degradation ratio lies below an explicit threshold determined by the inactivation and dimer-induced activation rates. Hence, the bimodality we observe can arise purely from stochastic effects rather than deterministic bistability. Our approach provides a general framework for diagnosing noise-induced multimodality in gene networks with nonlinear promoter transitions, without relying on exact probability distributions, which are typically infeasible for nonlinear reaction rates, particularly in our case. Beyond its theoretical contribution, this work has conceptual relevance to sustainability: our mode-detection diagnostics and the distinction between deterministic multistability and noise-induced multimodality can inform assessments of resilience, early-warning indicators, and state persistence.
{"title":"Noise-induced bimodality in self-regulated gene networks with nonlinear promoter transitions and fast dimerization.","authors":"Shih-Hsun Hung, Je-Chiang Tsai, Chih-Chi Wu","doi":"10.1007/s00285-026-02350-0","DOIUrl":"10.1007/s00285-026-02350-0","url":null,"abstract":"<p><p>We investigate noise-induced bimodal distributions in self-regulated gene networks with fast dimerization, where dimerized proteins enhance gene expression. Despite their fundamental role in gene regulation, analytical study of bimodal behaviour in such networks is challenging because the nonlinear interactions introduced by dimer formation render exact steady-state distributions infeasible. To address this, we reformulate the problem as a reduced self-regulated gene-expression model that approximates fast dimerization, in which the transition rate from the promoter-off to promoter-on state depends nonlinearly on protein levels. We introduce two diagnostic quantities: the promoter activity ratio, which quantifies promoter activation as a function of protein level, and the mode detection ratio, which identifies peaks of the steady-state protein distribution. Analysis of their recurrence relations reveals how promoter activity shapes the steady-state law, and how intrinsic stochasticity can generate multimodal protein distributions in self-regulated expression circuits. We further show that the corresponding mean-field ODE system admits a unique non-negative equilibrium when the protein synthesis-to-degradation ratio lies below an explicit threshold determined by the inactivation and dimer-induced activation rates. Hence, the bimodality we observe can arise purely from stochastic effects rather than deterministic bistability. Our approach provides a general framework for diagnosing noise-induced multimodality in gene networks with nonlinear promoter transitions, without relying on exact probability distributions, which are typically infeasible for nonlinear reaction rates, particularly in our case. Beyond its theoretical contribution, this work has conceptual relevance to sustainability: our mode-detection diagnostics and the distinction between deterministic multistability and noise-induced multimodality can inform assessments of resilience, early-warning indicators, and state persistence.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"92 2","pages":"31"},"PeriodicalIF":2.3,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12881043/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146133053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-06DOI: 10.1016/j.chaos.2026.117915
Guohui Li, Mingyao Zhang, Hong Yang
{"title":"Detection method of improved strongly coupled high-order Duffing-Van der Pol system for underwater acoustic signal","authors":"Guohui Li, Mingyao Zhang, Hong Yang","doi":"10.1016/j.chaos.2026.117915","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.117915","url":null,"abstract":"","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"95 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Numerical Analysis, Volume 64, Issue 1, Page 224-250, February 2026. Abstract. The numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance computation, these tasks are more complex due to the influence of surface geometry on the behavior of shortest paths. This paper introduces a primal-dual level set method for computing geodesic distances. A key insight is that the underlying surface can be implicitly represented as a zero level set, allowing us to formulate a constraint minimization problem. We employ the primal-dual methodology, along with regularization and acceleration techniques, to develop our algorithm. This approach is robust, efficient, and easy to implement. We establish a convergence result for the high resolution PDE system, and numerical evidence suggests that the method converges to a geodesic in the limit of refinement.
{"title":"A Primal-Dual Level Set Method for Computing Geodesic Distances","authors":"Hailiang Liu, Laura Zinnel","doi":"10.1137/24m1721086","DOIUrl":"https://doi.org/10.1137/24m1721086","url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 64, Issue 1, Page 224-250, February 2026. <br/> Abstract. The numerical computation of shortest paths or geodesics on surfaces, along with the associated geodesic distance, has a wide range of applications. Compared to Euclidean distance computation, these tasks are more complex due to the influence of surface geometry on the behavior of shortest paths. This paper introduces a primal-dual level set method for computing geodesic distances. A key insight is that the underlying surface can be implicitly represented as a zero level set, allowing us to formulate a constraint minimization problem. We employ the primal-dual methodology, along with regularization and acceleration techniques, to develop our algorithm. This approach is robust, efficient, and easy to implement. We establish a convergence result for the high resolution PDE system, and numerical evidence suggests that the method converges to a geodesic in the limit of refinement.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"89 1","pages":""},"PeriodicalIF":2.9,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146121993","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}
Pub Date : 2026-02-06DOI: 10.1016/j.jde.2026.114192
Qi Xiong , Zhenqiu Zhang , Lingwei Ma
In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the regularity criterion.
{"title":"Riesz potential estimates for double obstacle problems with Orlicz growth","authors":"Qi Xiong , Zhenqiu Zhang , Lingwei Ma","doi":"10.1016/j.jde.2026.114192","DOIUrl":"10.1016/j.jde.2026.114192","url":null,"abstract":"<div><div>In this paper, we consider the solutions to the non-homogeneous double obstacle problems with Orlicz growth involving measure data. After establishing the existence of the solutions to this problem in the Orlicz-Sobolev space, we derive a pointwise gradient estimate for these solutions by Riesz potential, which leads to the result on the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> regularity criterion.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"464 ","pages":"Article 114192"},"PeriodicalIF":2.3,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122593","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}
Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no analogues in the literature and rely on a new technique. The results are especially transparent for self-adjoint operators.
{"title":"On regularity of compressions and diagonals of operator functions","authors":"Vladimir Müller, Yuri Tomilov","doi":"10.1112/jlms.70433","DOIUrl":"https://doi.org/10.1112/jlms.70433","url":null,"abstract":"<p>Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no analogues in the literature and rely on a new technique. The results are especially transparent for self-adjoint operators.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"113 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146122844","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}
Pub Date : 2026-02-06DOI: 10.1016/j.jnt.2025.12.015
Iván Blanco-Chacón , Luis Dieulefait
Let be a totally real number field and an ideal of its ring of integers of norm N. Let be a prime totally split in F such that . For every even , define the -dimensional parallel weight . Let be any non CM Hilbert cuspidal Hecke eigenform. Assume that the residual representation has large image for some prime over p in the field of definition of f. Under these conditions, we prove that there exists a lift of associated to a Hilbert modular cuspform which is supercuspidal at each prime of F over p. We also give a proof of the corresponding statement for classical Hecke cuspforms. Such statement was already proved by Khare [23] with classical techniques. Finally, using our main result we give a corrigenda for [12], correctly inserting the micro good dihedral prime in the level.
{"title":"Modular supercuspidal lifts of weight 2","authors":"Iván Blanco-Chacón , Luis Dieulefait","doi":"10.1016/j.jnt.2025.12.015","DOIUrl":"10.1016/j.jnt.2025.12.015","url":null,"abstract":"<div><div>Let <span><math><mi>F</mi><mo>/</mo><mi>Q</mi></math></span> be a totally real number field and <span><math><mi>N</mi></math></span> an ideal of its ring of integers of norm <em>N</em>. Let <span><math><mi>p</mi><mo>></mo><mi>max</mi><mo></mo><mo>{</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>}</mo></math></span> be a prime totally split in <em>F</em> such that <span><math><mi>p</mi><mo>∤</mo><mi>N</mi></math></span>. For every even <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>, define the <span><math><mo>[</mo><mi>F</mi><mo>:</mo><mi>Q</mi><mo>]</mo></math></span>-dimensional parallel weight <span><math><mtext>k</mtext><mo>=</mo><mo>(</mo><mi>k</mi><mo>,</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>,</mo><mi>k</mi><mo>)</mo></math></span>. Let <span><math><mi>f</mi><mo>∈</mo><msub><mrow><mi>S</mi></mrow><mrow><mtext>k</mtext></mrow></msub><mo>(</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mi>N</mi><mo>)</mo><mo>)</mo></math></span> be any non CM Hilbert cuspidal Hecke eigenform. Assume that the residual representation <span><math><msub><mrow><mover><mrow><mi>ρ</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>f</mi><mo>,</mo><mi>P</mi></mrow></msub></math></span> has large image for some prime <span><math><mi>P</mi></math></span> over <em>p</em> in the field of definition of <em>f</em>. Under these conditions, we prove that there exists a lift of <span><math><msub><mrow><mover><mrow><mi>ρ</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>f</mi><mo>,</mo><mi>P</mi></mrow></msub></math></span> associated to a Hilbert modular cuspform <span><math><mi>g</mi><mo>∈</mo><msub><mrow><mi>S</mi></mrow><mrow><mtext>2</mtext></mrow></msub><mo>(</mo><mi>N</mi><msup><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo><mi>ϵ</mi><mo>)</mo></math></span> which is supercuspidal at each prime of <em>F</em> over <em>p</em>. We also give a proof of the corresponding statement for classical Hecke cuspforms. Such statement was already proved by Khare <span><span>[23]</span></span> with classical techniques. Finally, using our main result we give a corrigenda for <span><span>[12]</span></span>, correctly inserting the micro good dihedral prime in the level.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"285 ","pages":"Pages 54-73"},"PeriodicalIF":0.7,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146147486","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}
Pub Date : 2026-02-06DOI: 10.1016/j.chaos.2026.118026
Yiqun Yan, Qianwei Zhang, Leiman Fu
{"title":"The role of anxiety in the evolution of cooperative behavior based on spatial interactions","authors":"Yiqun Yan, Qianwei Zhang, Leiman Fu","doi":"10.1016/j.chaos.2026.118026","DOIUrl":"https://doi.org/10.1016/j.chaos.2026.118026","url":null,"abstract":"","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"48 1","pages":""},"PeriodicalIF":7.8,"publicationDate":"2026-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146134722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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