Physica D: Nonlinear Phenomena最新文献

{"title":"Discrete Lotka–Volterra systems with time delay and its stability analysis","authors":"Yusaku Yamamoto ,&nbsp;Taisei Yamamoto ,&nbsp;Takumi Kuroiwa ,&nbsp;Kurumi Oka ,&nbsp;Emiko Ishiwata ,&nbsp;Masashi Iwasaki","doi":"10.1016/j.physd.2025.134562","DOIUrl":"10.1016/j.physd.2025.134562","url":null,"abstract":"<div><div>We propose an extension of the discrete-time Lotka–Volterra (dLV) equations describing predator–prey dynamics with time delay <span><math><mi>τ</mi></math></span>. Introducing time delay corresponds to considering multiple generations of each species and gives more expressive power to the model. For example, it becomes possible to model the situation where each individual is eaten only after it has grown up. In this paper, we focus on the system with minimal time delay (<span><math><mrow><mi>τ</mi><mo>=</mo><mn>1</mn></mrow></math></span>) and analyze the stability of the system. In particular, we prove that when the number of species is three, the system exhibits the same asymptotic behavior as the original dLV system. For more general cases with an arbitrary odd number of species, we investigate the local stability of fixed points of the system with the help of the center manifold theory. It is shown that the fixed points that correspond to the asymptotic states of the original dLV system are locally stable.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134562"},"PeriodicalIF":2.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generalized Airy polynomials, Hankel determinants and asymptotics","authors":"Chao Min,&nbsp;Pixin Fang","doi":"10.1016/j.physd.2025.134560","DOIUrl":"10.1016/j.physd.2025.134560","url":null,"abstract":"<div><div>We further study the orthogonal polynomials with respect to the generalized Airy weight based on the work of Clarkson and Jordaan (2021). We prove the ladder operator equations and associated compatibility conditions for orthogonal polynomials with respect to a general Laguerre-type weight of the form <span><math><mrow><mi>w</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mi>λ</mi></mrow></msup><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>λ</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn><mo>,</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></mrow></math></span>. By applying them to the generalized Airy polynomials, we are able to derive a discrete system for the recurrence coefficients. Combining with the Toda evolution, we establish the relation between the recurrence coefficients, the sub-leading coefficient of the monic generalized Airy polynomials and the associated Hankel determinant. Using Dyson’s Coulomb fluid approach and with the aid of the discrete system for the recurrence coefficients, we obtain the large <span><math><mi>n</mi></math></span> asymptotic expansions for the recurrence coefficients and the sub-leading coefficient of the monic generalized Airy polynomials. The large <span><math><mi>n</mi></math></span> asymptotic expansion (including the constant term) of the Hankel determinant has been derived by using a recent result in the literature. The long-time asymptotics of these quantities have also been discussed explicitly.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134560"},"PeriodicalIF":2.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387311","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":"Exploring the synergy of media awareness and quarantine classes in SiSAQEIHR model for pandemic control: A Deep LSTM-RNN predictions","authors":"Anirban Tarafdar ,&nbsp;Jayanta Mahato ,&nbsp;Ranjit Kumar Upadhyay ,&nbsp;Paritosh Bhattacharya","doi":"10.1016/j.physd.2025.134563","DOIUrl":"10.1016/j.physd.2025.134563","url":null,"abstract":"<div><div>Media awareness and higher treatment rates are crucial in pandemics to prevent disease spread, but the synergy between quarantine and awareness is often neglected. This investigation explores the impact of media awareness on infectious diseases. For this purpose, a novel eight compartmental <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>i</mi></mrow></msub><mi>S</mi><mi>A</mi><mi>Q</mi><mi>E</mi><mi>I</mi><mi>H</mi><mi>R</mi></mrow></math></span> type mathematical model including eight individual classes, namely Immature Susceptible, Susceptible, Quarantine, Awareness, Exposed, Infective, Hospitality, and Recovered has been presented to depict disease dynamics. It incorporates a sigmoid type treatment rate, enhancing realism. This offers a fresh perspective on the study of infectious disease transmission. Mathematical analysis confirms the system’s positivity and boundedness, ensuring its theoretical stability analysis of the disease-free equilibrium point and applicability in predicting epidemic outcomes. Using the normalized forward sensitivity index, we have obtained sensitivity indices for factors associated with the basic reproduction number (<span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>) and identified the essential parameters that significantly impact the modification in disease dynamics. Also, the influence of the parameters on <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is systematically analyzed and characterized through Global Sensitivity Analysis. Furthermore, this study underscores the importance of accurately predicting epidemic spread to enable timely interventions, focusing on the pivotal roles of Awareness, Hospitalization, and Exposed classes in dynamic epidemic model. A deep Long Short-Term Memory (LSTM) based Recurrent Neural Network (RNN) model is proposed for precise spread pattern prediction, leveraging advanced deep learning capabilities in time series analysis. Six hyperparameter topologies are analyzed to optimize prediction accuracy. Five statistical accuracy metrics reveal RMSE below 0.02 and <span><math><mi>R</mi></math></span> and <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> values exceeding 0.99 for all classes, validating satisfactory predictive performance. A real-life COVID-19 modeling study demonstrates the proposed LSTM-based model’s effectiveness in capturing complex dynamics, surpassing earlier traditional neural network methods. Furthermore, sensitivity analysis, varying the vaccinated proportion, confirms the robustness of the proposed model system in the realm of public health decision-making.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134563"},"PeriodicalIF":2.7,"publicationDate":"2025-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403402","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":"Probability distribution in the Toda system: The singular route to a steady state","authors":"Srdjan Petrović ,&nbsp;Nikola Starčević ,&nbsp;Nace Stojanov ,&nbsp;Liang Huang","doi":"10.1016/j.physd.2025.134576","DOIUrl":"10.1016/j.physd.2025.134576","url":null,"abstract":"<div><div>This study reports on the evolution of the probability distribution in the configuration space of the two-dimensional Toda system. The distribution is characterized by singularities, which predominantly take two forms: double-cusped triangular lines and lines parallel to the equipotential line that defines the accessible region. Over time, the number of these singular patterns increases linearly. Consequently, at very large times, the singular patterns fully occupy the accessible area, resulting in a steady state probability distribution with a pronounced singular peak at the center.</div><div>Changes in the singular patterns arise solely from the system's intrinsic dynamics rather than variations in its parameters, emphasizing the system's self-organizing nature over time. These results provide a deeper understanding of the collective motion of particles in symmetric, bounded, two-dimensional conservative systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134576"},"PeriodicalIF":2.7,"publicationDate":"2025-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387312","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":"Effects of nonlinear coupling parameters on the formation of intrinsic localized modes in a quantum 1D mixed Klein–Gordon/Fermi–Pasta–Ulam chain","authors":"R. Abouem A Ribama ,&nbsp;Z.I. Djoufack ,&nbsp;J.P. Nguenang","doi":"10.1016/j.physd.2025.134556","DOIUrl":"10.1016/j.physd.2025.134556","url":null,"abstract":"<div><div>We analyze the effects of the nonlinear coupling parameters <span><math><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> on the formation of intrinsic localized modes (ILMs) in a one-dimensional quantum mixed Klein–Gordon/Fermi–Pasta–Ulam (KG/FPU) chain. Our results indicate that the frequency amplitude is more significantly affected by increasing the values of the nonlinear parameter <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> compared to the parameter <span><math><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>. Additionally, we demonstrate that the mixed system admits breather solutions known as ILMs, with energy exhibiting symmetrical properties. Numerical simulations conducted to support our analytical findings reveal that the <span><math><msub><mrow><mi>k</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> parameter in the KG potential leads to minimal scattering of phonons, while the <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> parameter in the FPU potential results in strong phonon scattering phenomena in the mixed KG/FPU system. Furthermore, we confirm the existence of ILMs through a linear stability analysis, deriving the criteria for the appearance of modulational instability (MI). Our findings show that the shape of MI regions and the instability growth rate are significantly influenced by increases in the nonlinear parameter <span><math><msub><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>. The theoretical predictions have been validated through numerical tests using the discrete spatial Fourier method, demonstrating full agreement with our analytical results.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134556"},"PeriodicalIF":2.7,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143378667","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":"Nonlinearity mediated miscibility dynamics of mass-imbalanced binary Bose–Einstein condensate for circular atomtronics","authors":"Sriganapathy Raghav ,&nbsp;Suranjana Ghosh ,&nbsp;Barun Halder ,&nbsp;Utpal Roy","doi":"10.1016/j.physd.2025.134558","DOIUrl":"10.1016/j.physd.2025.134558","url":null,"abstract":"<div><div>We explore the nonlinearity-induced and fractional revivals-driven miscibility dynamics of quasi-2D mass-imbalanced binary Bose–Einstein condensates, confined in a ring-shaped waveguide. During their time-evolution, the two condensate species generally remain miscible, as observed in the spatial density distributions and the autocorrelation functions. Although, the investigation is carried out for a wide range of mass-imbalance, initial demonstration is focussed on insignificant mass-imbalance of the two <span><math><mrow><mi>R</mi><mi>b</mi></mrow></math></span>-isotopes with suitable experimental parameters. The characteristic time scales are influenced by the trap parameters and the strengths of nonlinearities. The study also reveals the conditions under which the condensates become spatially distinguishable with clear signatures in their autocorrelation functions. A separability function further identifies favourable parameters and the fractional revival instances for greater separability. We report precise range of the ring-radius and the interaction strength for experimental realization. Additionally, the average separability variation reflects the result across a variety of condensate species.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134558"},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143396156","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":"Rogue wave solutions to the coupled Sasa–Satsuma equation","authors":"Guangxiong Zhang ,&nbsp;Xiyao Chen ,&nbsp;Bao-Feng Feng ,&nbsp;Chengfa Wu","doi":"10.1016/j.physd.2025.134549","DOIUrl":"10.1016/j.physd.2025.134549","url":null,"abstract":"<div><div>In this paper, general rogue wave solutions to the coupled Sasa–Satsuma (CSS) equation are constructed by the Kadomtsev–Petviashvili (KP) reduction method. These rogue wave solutions are classified into three families, which correspond to one complex simple root, two complex simple roots, and one complex double root of an octic algebraic equation related to the dimension reduction condition, respectively. All of these complex roots should have nonzero real and imaginary parts. Furthermore, by considering the case where either only real roots or both real and complex roots of the aforementioned octic algebraic equation are present, other rational solutions such as W-shaped soliton and the mixture of W-shaped soliton and rogue wave solutions to the CSS equation are derived and illustrated.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134549"},"PeriodicalIF":2.7,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403403","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":"Influence of coupling symmetries and noise on the critical dynamics of synchronizing oscillator lattices","authors":"Ricardo Gutiérrez,&nbsp;Rodolfo Cuerno","doi":"10.1016/j.physd.2025.134552","DOIUrl":"10.1016/j.physd.2025.134552","url":null,"abstract":"<div><div>Recent work has shown that the synchronization process in lattices of self-sustained (phase and limit-cycle) oscillators displays universal scale-invariant behavior previously studied in the physics of surface kinetic roughening. The type of dynamic scaling ansatz which is verified depends on the randomness that occurs in the system, whether it is columnar disorder (quenched noise given by the random assignment of natural frequencies), leading to anomalous scaling, or else time-dependent noise, inducing the more standard Family-Vicsek dynamic scaling ansatz, as in equilibrium critical dynamics. The specific universality class also depends on the coupling function: for a sine function (as in the celebrated Kuramoto model) the critical behavior is that of the Edwards-Wilkinson equation for the corresponding type of randomness, with Gaussian fluctuations around the average growth. In all the other cases investigated, Tracy–Widom fluctuations ensue, associated with the celebrated Kardar–Parisi–Zhang equation for rough interfaces. Two questions remain to be addressed in order to complete the picture, however: (1) Is the atypical scaling displayed by the sine coupling preserved if other coupling functions satisfying the same (odd) symmetry are employed (as suggested by continuum approximations and symmetry arguments)? and (2) how does the competition between both types of randomness (which are expected to coexist in experimental settings) affect the nonequilibrium behavior? We address the latter question by numerically characterizing the crossover between thermal-noise and columnar-disorder criticality, and the former by providing evidence confirming that it is the symmetry of the coupling function that sets apart the sine coupling, among other odd-symmetric couplings, due to the absence of Kardar–Parisi–Zhang fluctuations.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134552"},"PeriodicalIF":2.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143372041","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":"Revisiting viscoelastic liquid films flowing down a slippery substrate: Linear and nonlinear viscoelastic waves","authors":"Zhiwei Song ,&nbsp;Zijing Ding","doi":"10.1016/j.physd.2025.134554","DOIUrl":"10.1016/j.physd.2025.134554","url":null,"abstract":"<div><div>This paper revisits the flow of a viscoelastic film on a slippery substrate (Phys. Rev. Fluids <strong>7</strong> (6), 064007, 2022) using the Navier-slip boundary condition, <span><math><mrow><msub><mrow><mi>τ</mi></mrow><mrow><mi>x</mi><mi>z</mi></mrow></msub><mo>=</mo><mi>λ</mi><mi>u</mi></mrow></math></span> (<span><math><mi>λ</mi></math></span> represents the friction coefficient of the substrate). Here, <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>x</mi><mi>z</mi></mrow></msub></math></span> represents the total tangential shear stress, comprised of both a viscous and an elastic component. A model equation for the film thickness is derived based on the long-wave theory. The study investigates both the linear and nonlinear dynamics of the film flow. It reveals that the presence of a slippery substrate and viscoelasticity promote the instability of linear viscoelastic waves. Additionally, they affect the speed and height of nonlinear viscoelastic waves. Our present study suggests that neglecting the elastic component of <span><math><msub><mrow><mi>τ</mi></mrow><mrow><mi>x</mi><mi>z</mi></mrow></msub></math></span> at the slippery wall could result in an overestimation of the linear stability threshold while underestimating the speed and height of nonlinear waves.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134554"},"PeriodicalIF":2.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143345896","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":"Garden of bifurcating paths in a nonlinear optical system","authors":"Lucas Sarrazin ,&nbsp;Mathias Marconi ,&nbsp;Massimo Giudici ,&nbsp;Myriam Nonaka ,&nbsp;Monica Agüero ,&nbsp;Alejandro Hnilo ,&nbsp;Marcelo Kovalsky ,&nbsp;Karin Alfaro-Bittner ,&nbsp;Jorge Tredicce","doi":"10.1016/j.physd.2025.134553","DOIUrl":"10.1016/j.physd.2025.134553","url":null,"abstract":"<div><div>We study both theoretically and experimentally the dynamical behavior of a Class B laser with modulated losses. We focus our attention on the response of the system as we sweep the modulation frequency. The nonlinearity of the system introduces a multistability of the laser intensity at resonance but also at subharmonics of the resonance and at harmonics of it. In general subharmonics and harmonics resonances in conjunction with low dissipation are at the origin of multistability in nonlinear dynamical systems. We show the response in intensity for low values of the modulation amplitude. We put in evidence the generation of harmonics of the modulation frequency at subharmonics resonances of the system. The experimental results are in very good agreement with the numerical results obtained from the most simple dynamical model for such type of lasers.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134553"},"PeriodicalIF":2.7,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376742","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}