Physica D: Nonlinear Phenomena最新文献

{"title":"Detecting imbalanced financial markets through time-varying optimization and nonlinear functionals","authors":"Nick James ,&nbsp;Max Menzies","doi":"10.1016/j.physd.2025.134571","DOIUrl":"10.1016/j.physd.2025.134571","url":null,"abstract":"<div><div>This paper studies the time-varying structure of the equity market with respect to market capitalization. First, we analyze the distribution of the 100 largest companies’ market capitalizations over time, in terms of inequality, concentration at the top, and overall discrepancies in the distribution between different times. In the next section, we introduce a mathematical framework of linear and nonlinear functionals of time-varying portfolios. We apply this to study the market capitalization exposure and spread of optimal portfolios chosen by a Sharpe optimization procedure. These methods could be more widely used to study various measures of optimal portfolios and measure different aspects of market exposure while holding portfolios selected by an optimization routine that changes over time.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134571"},"PeriodicalIF":2.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436772","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":"Shock selection in reaction–diffusion equations with partially negative diffusivity using nonlinear regularisation","authors":"Thomas Miller ,&nbsp;Alexander K.Y. Tam ,&nbsp;Robert Marangell ,&nbsp;Martin Wechselberger ,&nbsp;Bronwyn H. Bradshaw-Hajek","doi":"10.1016/j.physd.2025.134561","DOIUrl":"10.1016/j.physd.2025.134561","url":null,"abstract":"<div><div>Solutions to reaction–nonlinear-diffusion (RND) equations with a region of negative diffusivity exhibit shocks. In general, the position of these shocks can vary, necessitating selection criteria to determine a unique shock. Previous studies have defined conditions for shock selection. A common choice is the equal area rule, which corresponds to a fourth-order non-local regularisation to the RND equation. Bradshaw-Hajek et al. (2024) showed that combining non-local and viscous regularisations can yield a continuum of possible shocks. In this work, we demonstrate how to achieve a continuum of shocks using a single nonlinear regularisation term. With one nonlinear regularisation, shock selection obeys a modified equal area rule, where adjusting the nonlinearity in the regularisation moves the shock. To demonstrate the technique, we attain solutions with conserved diffusivity across the shock, which yield the longest shock length possible. Using geometric singular perturbation theory, we prove the existence of travelling waves with continuous diffusivity shocks. Numerical solutions align with theoretical predictions for shock position and wave speed.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134561"},"PeriodicalIF":2.7,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436771","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":"Quasi-periodic swing via weak KAM theory","authors":"Xun Niu ,&nbsp;Kaizhi Wang ,&nbsp;Yong Li","doi":"10.1016/j.physd.2025.134559","DOIUrl":"10.1016/j.physd.2025.134559","url":null,"abstract":"<div><div>Our primary focus is on the study of the dynamics of quasi-periodic swing equations from the weak KAM point of view. To achieve this, we initially explore a class of quasi-periodic Hamiltonian systems. We discover that a limit function, derived from the convergence of a sequence of functional minimizers, satisfies the Hamilton–Jacobi equations in the context of minimal measures. This is the so-called weak KAM solution. Subsequently, we establish the existence of invariant torus for the swing equation in a weak sense. Lastly, we discuss certain properties of the weak KAM solution for a one-dimensional periodic swing equation.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"474 ","pages":"Article 134559"},"PeriodicalIF":2.7,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420670","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":"Thermal lifetime of breathers","authors":"Juan F.R. Archilla ,&nbsp;Jānis Bajārs ,&nbsp;Sergej Flach","doi":"10.1016/j.physd.2025.134551","DOIUrl":"10.1016/j.physd.2025.134551","url":null,"abstract":"<div><div>In this article, we explore the lifetime of localized excitations in nonlinear lattices, called breathers, when a thermalized lattice is perturbed with localized energy delivered to a single site. We develop a method to measure the time it takes for the system to approach equilibrium based on a single scalar quantity, the participation number, and deduce the value corresponding to thermal equilibrium. We observe the time to achieve thermalization as a function of the energy of the excited site. We explore a variety of different physical system models. The result is that the lifetime of breathers increases exponentially with the breather energy for all the systems. This increase becomes observable when this energy is larger than approximately ten times the local average thermal energy. These results may provide a method to detect the existence of breathers in real systems.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"473 ","pages":"Article 134551"},"PeriodicalIF":2.7,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395971","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":"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}