数学最新文献

{"title":"Geometric nonlinear dynamics of a quasi-zero stiffness isolator integrated with an energy harvester: Monostable, perfect zero-linear stiffness, and bistable oscillation modes","authors":"Nasser A. Saeed ,&nbsp;Y.Y. Ellabban ,&nbsp;Lei Hou ,&nbsp;Shun Zhong ,&nbsp;Faisal Z. Duraihem","doi":"10.1016/j.chaos.2025.116633","DOIUrl":"10.1016/j.chaos.2025.116633","url":null,"abstract":"<div><div>Achieving effective vibration isolation across a broad frequency range while simultaneously harvesting energy from vibrations remains a key challenge in engineering systems. This study examines the nonlinear dynamics and vibration isolation performance of an oblique-type spring quasi-zero stiffness (QZS) isolator integrated with a piezoelectric energy harvester. The coupled system is modeled as a strongly nonlinear oscillator linked to a first-order differential equation governing the harvester's response. The QZS isolator's behavior is characterized by two geometric nonlinearity parameters, the stiffness ratio of oblique to vertical springs (<span><math><mi>ρ</mi></math></span>) and the ratio of the oblique spring's maximum horizontal compression to its free length (<span><math><mi>λ</mi></math></span>). Closed-form expressions for <span><math><mi>ρ</mi></math></span> and <span><math><mi>λ</mi></math></span> are derived to determine the conditions for monostable, bistable, and perfect zero-linear stiffness operation. The system's response is analyzed using the harmonic balance method, with bifurcation diagrams illustrating oscillation amplitudes, harvested voltage, and displacement transmissibility under different excitation conditions. Key findings indicate that for <span><math><mi>ρ</mi><mo>&lt;</mo><mi>λ</mi><mo>/</mo><mfenced><mrow><mn>2</mn><mo>−</mo><mn>2</mn><mi>λ</mi></mrow></mfenced></math></span>, the system functions as a monostable QZS isolator, where reducing <span><math><mi>λ</mi></math></span> and/or increasing <span><math><mi>ρ</mi></math></span> suppresses resonant peaks, creating a semi-full-band isolator. When <span><math><mi>ρ</mi><mo>=</mo><mi>λ</mi><mo>/</mo><mfenced><mrow><mn>2</mn><mo>−</mo><mn>2</mn><mi>λ</mi></mrow></mfenced></math></span>, the system achieves full-band vibration isolation with perfect zero-linear stiffness, enhanced by high pre-compression of the oblique springs. For <span><math><mi>ρ</mi><mo>&gt;</mo><mi>λ</mi><mo>/</mo><mfenced><mrow><mn>2</mn><mo>−</mo><mn>2</mn><mi>λ</mi></mrow></mfenced></math></span>, the system transitions to a bistable regime, improving energy harvesting but reducing isolation efficiency. Additionally, the piezoelectric harvester not only facilitates energy conversion but also introduces active damping, effectively mitigating resonant peaks and stabilizing the system under strong base excitations while minimally affecting high-frequency displacement transmissibility. This work provides a comprehensive understanding of the oscillation modes in oblique-type QZS systems and offers design insights for optimizing geometric parameters to achieve full-band or semi-full-band isolation and efficient energy harvesting.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116633"},"PeriodicalIF":5.3,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144166080","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}

{"title":"On strong odd colorings of graphs","authors":"Yair Caro ,&nbsp;Mirko Petruševski ,&nbsp;Riste Škrekovski ,&nbsp;Zsolt Tuza","doi":"10.1016/j.disc.2025.114601","DOIUrl":"10.1016/j.disc.2025.114601","url":null,"abstract":"<div><div>A strong odd coloring of a simple graph <em>G</em> is a proper coloring of the vertices of <em>G</em> such that for every vertex <em>v</em> and every color <em>c</em>, either <em>c</em> is used an odd number of times in the open neighborhood <span><math><msub><mrow><mi>N</mi></mrow><mrow><mi>G</mi></mrow></msub><mo>(</mo><mi>v</mi><mo>)</mo></math></span> or no neighbor of <em>v</em> is colored by <em>c</em>. The smallest integer <em>k</em> for which <em>G</em> admits a strong odd coloring with <em>k</em> colors is the strong odd chromatic number, <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>so</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. These coloring notion and graph parameter were recently defined in Kwon and Park (<span><span>arXiv:2401.11653</span><svg><path></path></svg></span>). We answer a question raised by the originators concerning the existence of a constant bound for the strong odd chromatic number of all planar graphs. We also consider strong odd colorings of trees, unicyclic graphs, claw-free graphs, and graph products.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 11","pages":"Article 114601"},"PeriodicalIF":0.7,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144170355","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}

{"title":"Effect of malicious cyber-attack on jamming transition in a multi-phase mixed flow model under regular vehicles and connected vehicles environment","authors":"Yi Tang ,&nbsp;Cong Zhai ,&nbsp;Yingping Xiao ,&nbsp;Min Zhai ,&nbsp;Jiyong Zhang","doi":"10.1016/j.chaos.2025.116665","DOIUrl":"10.1016/j.chaos.2025.116665","url":null,"abstract":"<div><div>With the promotion of policies and technological progress, accelerate the advancement of Internet of Vehicles (IOVs) and refine it considerably, and then the real-time communication of vehicle-vehicle, vehicle-infrastructure and vehicle cloud will be realized, which will provide more abundant data for connected vehicles (CVs); however, the large-scale popularization of the vehicle was a drawn-out procedure, and regular vehicles (RVs) and connected vehicles will share road infrastructure within this duration. Aiming at the significant distinctions in exogenous information acquisition mode between the two types of vehicles, and considering that the latter is vulnerable to cyber-attacks from hackers when it plays the advantage of information sharing in an open workshop communication environment. Motivation by this, we extended the optimal velocity car-following model and provided an original mixed-flow model accounting for the malicious cyber-attack effect, moreover, introducing a multi-phase optimal velocity function to describe the discontinuous acceleration phenomenon in real traffic. In the linear stability analysis part, we employ the reductive perturbation approaches to figure out the stability requirement for the new model, which reveals that the permeability of CVs and the intensity of cyber-attacks have a substantial influence on the traffic dynamics, and the number of phases of transition stages highly dependent on the count of the turning points in the optimal velocity function; subsequently, in the nonlinear analysis part, the modified Korteweg-de Vries (mKdV) equation is developed to illustrate the emerge and spatiotemporal progression of traffic jams when stability criteria is not achieved. At last, the above theoretical arguments are supported by the numerical simulation results.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"199 ","pages":"Article 116665"},"PeriodicalIF":5.3,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167215","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}

{"title":"A memristive neuron with double capacitive variables coupled by Josephson junction","authors":"Binchi Wang ,&nbsp;Guodong Ren ,&nbsp;Jun Ma ,&nbsp;Yitong Guo","doi":"10.1016/j.chaos.2025.116630","DOIUrl":"10.1016/j.chaos.2025.116630","url":null,"abstract":"<div><div>Continuous firing patterns in biological neurons result from time-varying electromagnetic field accompanied by energy exchange between magnetic field and electric field in the cell, which the intracellular ions are diffused and membrane channels are open for ions propagation across the outer and inner cell membranes. Incorporation of memristive terms of the neuron models can describe the effect of electromagnetic induction and even the regulation from external applied physical field. During circuit approach and implement for a neural circuit, capacitors are used to mimic the capacitive properties of the cell membrane, while inductors, nonlinear resistor and constant voltage source are effective to mimic the physical properties of ion channels. This paper proposed a neural circuit composed of two capacitors via Josephson junction connection, and the paralleled branch circuits are connected by using an inductor and a memristor. The absence using of both linear and nonlinear resistors reduces consumption of Joule heat. Energy function for the two kinds of memristive neurons are obtained and proofed, stochastic/coherence resonance is induced under noisy excitation at moderate noise intensity. Stability and bifurcation analysis clarified the main dynamical and physical property of the suggested neural circuits and their equivalent dimensionless models. Finally, an adaptive growth law is suggested to control the membrane parameter and mode transition between firing patterns is discussed in detail. That is, the neural circuit coupled with memristor and Josephson junction is effective to describe the electrical property and dynamical characteristic even without using any resistive components.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"198 ","pages":"Article 116630"},"PeriodicalIF":5.3,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168290","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}

{"title":"Oscillation theory for linear evolution processes","authors":"M.Ap. Silva ,&nbsp;E.M. Bonotto ,&nbsp;M. Federson","doi":"10.1016/j.jde.2025.113464","DOIUrl":"10.1016/j.jde.2025.113464","url":null,"abstract":"<div><div>We introduce the theory of pullback oscillation for linear evolution processes. Necessary and sufficient conditions are presented to obtain pullback oscillation via geometric interpretation of the closed conic hull. Using the theory of generalized ODEs, we apply the main results to a class of abstract ordinary differential equations, as well as to Volterra-Stieltjes-type integral equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"440 ","pages":"Article 113464"},"PeriodicalIF":2.4,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169295","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}

{"title":"Structural identifiability of linear-in-parameter parabolic PDEs through auxiliary elliptic operators.","authors":"Yurij Salmaniw, Alexander P Browning","doi":"10.1007/s00285-025-02225-w","DOIUrl":"https://doi.org/10.1007/s00285-025-02225-w","url":null,"abstract":"<p><p>Parameter identifiability is often requisite to the effective application of mathematical models in the interpretation of biological data, however theory applicable to the study of partial differential equations remains limited. We present a new approach to structural identifiability analysis of fully observed parabolic equations that are linear in their parameters. Our approach frames identifiability as an existence and uniqueness problem in a closely related elliptic equation and draws, for homogeneous equations, on the well-known Fredholm alternative to establish unconditional identifiability, and cases where specific choices of initial and boundary conditions lead to non-identifiability. While in some sense pathological, we demonstrate that this loss of structural identifiability has ramifications for practical identifiability; important particularly for spatial problems, where the initial condition is often limited by experimental constraints. For cases with nonlinear reaction terms, uniqueness of solutions to the auxiliary elliptic equation corresponds to identifiability, often leading to unconditional global identifiability under mild assumptions. We present analysis for a suite of simple scalar models with various boundary conditions that include linear (exponential) and nonlinear (logistic) source terms, and a special case of a two-species cell motility model. We conclude by discussing how this new perspective enables well-developed analysis tools to advance the developing theory underlying structural identifiability of partial differential equations.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 1","pages":"4"},"PeriodicalIF":2.2,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144175700","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Steady compressible 3D Euler flows in toroidal volumes without continuous Euclidean isometries","authors":"Naoki Sato ,&nbsp;Michio Yamada","doi":"10.1016/j.physd.2025.134741","DOIUrl":"10.1016/j.physd.2025.134741","url":null,"abstract":"<div><div>We demonstrate the existence of smooth three-dimensional vector fields where the cross product between the vector field and its curl is balanced by the gradient of a smooth function, with toroidal level sets that are not invariant under continuous Euclidean isometries. This finding indicates the existence of steady compressible Euler flows, either influenced by an external potential energy or maintained by a density source in the continuity equation, that are foliated by asymmetric nested toroidal surfaces. Our analysis suggests that the primary obstacle in resolving Grad’s conjecture regarding the existence of nontrivial magnetohydrodynamic equilibria arises from the incompressibility constraint imposed on the magnetic field.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"480 ","pages":"Article 134741"},"PeriodicalIF":2.7,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169732","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}

{"title":"Driven transitions between megastable quantized orbits","authors":"Álvaro G. López ,&nbsp;Rahil N. Valani","doi":"10.1016/j.chaos.2025.116549","DOIUrl":"10.1016/j.chaos.2025.116549","url":null,"abstract":"<div><div>We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, <em>i.e.</em> megastability. In the low-memory regime, the equation reduces to a self-excited nonlinear oscillator and we use averaging methods to analytically show quasilinear increasing amplitude of the megastable spectrum of quantized quasicircular orbits. We further assign a mechanical energy to each orbit using the Lyapunov energy function and obtain a quadratically increasing energy spectrum and (almost) constant frequency spectrum. We demonstrate transitions between different quantized orbits, i.e. different energy levels, by subjecting the system to an external finite-time harmonic driving. In the absence of external driving force, the oscillator asymptotes towards one of the megastable quantized orbits having a fixed average energy. For a large driving amplitude with frequency close to the limit cycle frequency, resonance drives transitions to higher energy levels. Alternatively, for large driving amplitude with frequency slightly detuned from limit-cycle frequency, beating effects can lead to transitions to lower energy levels. Such driven transitions between quantized orbits form a classical analog of quantum jumps. For excitations to higher energy levels, we show amplitude locking where nearby values of driving amplitudes result in the same response amplitude, i.e. the same final higher energy level. We rationalize this effect based on the basins of different limit cycles in phase space. From a practical viewpoint, our work might find applications in physical and engineering system where controlled transitions between several limit cycles of a multistable dynamical system is desired.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"198 ","pages":"Article 116549"},"PeriodicalIF":5.3,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168289","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}

{"title":"Turbulent waves and oscillating amplitude of boundary-layers and radiative-heat transfer of nonlinear Williamson nanofluid over solar plate with periodic conditions","authors":"Zia Ullah ,&nbsp;Md. Mahbub Alam ,&nbsp;Bagh Ali ,&nbsp;Ramzi Rzig ,&nbsp;Hanaa Abu-Zinadah ,&nbsp;Mohamed Boujelbene ,&nbsp;Nidhal Ben Khedher","doi":"10.1016/j.chaos.2025.116639","DOIUrl":"10.1016/j.chaos.2025.116639","url":null,"abstract":"<div><div>Turbulence and oscillating amplitude of boundary layers and nonlinear radiative heat and concentration motion of transient Williamson nanomaterial model alongside inclined solar surface with entropy optimization, magnetic oscillation, dynamic solar energy, and thermo diffusion is the novelty of this work. The objective of this problem is to scrutinize the speed streamlines, isothermal lines, energy/temperature and mass/concentration fields, steady heating ratio and instability of fluctuating energy/heat transfer alongside inclined plate at angle π/4. Governing mathematical formulation is developed to find the numerical outcomes of unknown physical properties. Fluctuating Stokes transformations and dimensionless variables are developed to reduce governing equations into oscillatory and steady equations with defined boundary values. Various pertinent parameters are generated for physical analysis of heat rate such as Eckert number (<span><math><msub><mi>E</mi><mi>c</mi></msub></math></span>), buoyancy number (<span><math><msub><mi>λ</mi><mi>T</mi></msub></math></span>), oscillating magnetic parameter (<span><math><msub><mi>M</mi><mi>f</mi></msub></math></span>), Schmidt number (<span><math><msub><mi>S</mi><mi>c</mi></msub></math></span>), radiation number (<span><math><msub><mi>R</mi><mi>d</mi></msub></math></span>), thermophoresis number (<span><math><msub><mi>N</mi><mi>T</mi></msub></math></span>), Prandtl number (<em>Pr</em>), and Brownian motion number (<span><math><msub><mi>N</mi><mi>b</mi></msub></math></span>). Primitive variable transformation is applied to generate symmetry in all governing equations in FORTRAN programming tool for accurate asymptotic results. Implicit formula of finite difference scheme with central and backward relation is used to convert system of equations into algebraic equations. The obtained algebraic equations are solved through Gaussian elimination technique to explore fluid flow, heat and mass rate, and periodical fluctuations in thermal and concentration gradients. It is perceived that high largeness in fluid speed and energy/temperature field is depicted as thermal radiating constraint upsurges. The magnitude of streamlines ad isothermal lines is decreased as oscillating magnetic number and Eckert number increases but isothermal lines increased with maximum strong magnetic field. High oscillations in turbulent behavior of fluctuating heat and concentration/mass removal is noted for each value of magnetic field and Weissenberg number.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"198 ","pages":"Article 116639"},"PeriodicalIF":5.3,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168297","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}

{"title":"HIV dynamics under multi-drug combination therapy: mathematical modelling and data fitting.","authors":"Ning Bai, Rui Xu","doi":"10.1007/s00285-025-02232-x","DOIUrl":"https://doi.org/10.1007/s00285-025-02232-x","url":null,"abstract":"<p><p>The Manual of National Free AIDS Antiviral Drug Treatment (version 2023), compiled by the National Center for AIDS/STD Control and Prevention, China CDC, recommends that the preferred first-line treatment regimen for drug-naive, HIV-infected individuals be a combination of tenofovir disoproxil fumarate (TDF), lamivudine (3TC) and efavirenz (EFV). Now two questions arise: why should multi-drug combination therapy be used to suppress the viral load in patients? What are the impacts of different medication regimens on the viral load dynamics? To this end, we consider a within-host HIV infection model coupling viral dynamics and pharmacokinetics, where the time evolution of drug concentration is described by a two-compartment model with extravascular drug delivery route. Based on the actual data, we apply the Markov-chain Monte-Carlo (MCMC) method containing the Metropolis-Hastings (M-H) algorithm to estimate the unknown parameters in pretreatment model of HIV infection and pharmacokinetics model, respectively. Subsequently, based on the estimated parameters, numerical results suggest that: (i) in the case of monotherapy, the viral load in patients can be completely suppressed if the first-line treatment regimen is strictly followed, but the impact of medication adherence on antiviral response is more obvious; (ii) in the case of multi-drug combination therapy, the impact of medication adherence on antiviral response is diminished compared to monotherapy; (iii) early initiation of the first-line treatment helps to ensure the success of treatment. This study reveals the time evolution of viral load under antiviral therapy, evaluates the effectiveness and potential risks of treatment, and provides guidance for the clinical treatment.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 1","pages":"5"},"PeriodicalIF":2.2,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144175699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}