Journal of Nonlinear Science最新文献

{"title":"Elastic Metrics on Spaces of Euclidean Curves: Theory and Algorithms","authors":"Martin Bauer, Nicolas Charon, Eric Klassen, Sebastian Kurtek, Tom Needham, Thomas Pierron","doi":"10.1007/s00332-024-10035-5","DOIUrl":"https://doi.org/10.1007/s00332-024-10035-5","url":null,"abstract":"<p>A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis framework is to define such a metric by starting with a reparametrization-invariant Riemannian metric on the space of parametrized shapes and inducing a metric on the quotient by the group of diffeomorphisms. This quotient metric is computed, in practice, by finding a registration of two shapes over the diffeomorphism group. For spaces of Euclidean curves, the initial Riemannian metric is frequently chosen from a two-parameter family of Sobolev metrics, called elastic metrics. Elastic metrics are especially convenient because, for several parameter choices, they are known to be locally isometric to Riemannian metrics for which one is able to solve the geodesic boundary problem explicitly—well-known examples of these local isometries include the complex square root transform of Younes, Michor, Mumford and Shah and square root velocity (SRV) transform of Srivastava, Klassen, Joshi and Jermyn. In this paper, we show that the SRV transform extends to elastic metrics for all choices of parameters, for curves in any dimension, thereby fully generalizing the work of many authors over the past two decades. We give a unified treatment of the elastic metrics: we extend results of Trouvé and Younes, Bruveris as well as Lahiri, Robinson and Klassen on the existence of solutions to the registration problem, we develop algorithms for computing distances and geodesics, and we apply these algorithms to metric learning problems, where we learn optimal elastic metric parameters for statistical shape analysis tasks.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806816","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":"A Generalized Sine-Gordon Equation: Reductions and Integrable Discretizations","authors":"Han-Han Sheng, Bao-Feng Feng, Guo-Fu Yu","doi":"10.1007/s00332-024-10030-w","DOIUrl":"https://doi.org/10.1007/s00332-024-10030-w","url":null,"abstract":"<p>In this paper, we propose fully discrete analogues of a generalized sine-Gordon (gsG) equation <span>(u_{t x}=left( 1+nu partial _x^2right) sin u)</span>. The key points of the construction are based on the bilinear discrete KP hierarchy and appropriate definition of discrete reciprocal transformations. We derive semi-discrete analogues of the gsG equation from the fully discrete gsG equation by taking the temporal parameter limit <span>(brightarrow 0)</span>. In particular, one fully discrete gsG equation is reduced to a semi-discrete gsG equation in the case of <span>(nu =-1)</span> (Feng et al. in Numer Algorithms 94:351–370, 2023). Furthermore, <i>N</i>-soliton solutions to the semi- and fully discrete analogues of the gsG equation in the determinant form are presented. Dynamics of one- and two-soliton solutions for the discrete gsG equations are analyzed. By introducing a parameter <i>c</i>, we demonstrate that the gsG equation can reduce to the sine-Gordon equation and the short pulse at the levels of continuous, semi-discrete and fully discrete cases. The limiting forms of the <i>N</i>-soliton solutions to the gsG equation in each level also correspond to those of the sine-Gordon equation and the short pulse equation.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140609412","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":"2D Smagorinsky-Type Large Eddy Models as Limits of Stochastic PDEs","authors":"Franco Flandoli, Dejun Luo, Eliseo Luongo","doi":"10.1007/s00332-024-10028-4","DOIUrl":"https://doi.org/10.1007/s00332-024-10028-4","url":null,"abstract":"<p>We prove that a version of Smagorinsky large eddy model for a 2D fluid in vorticity form is the scaling limit of suitable stochastic models for large scales, where the influence of small turbulent eddies is modeled by a transport-type noise.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575854","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":"Strong Symmetry Breaking in Coupled, Identical Lengyel–Epstein Oscillators via Folded Singularities","authors":"Naziru M. Awal, Irving R. Epstein, Tasso J. Kaper, Theodore Vo","doi":"10.1007/s00332-024-10033-7","DOIUrl":"https://doi.org/10.1007/s00332-024-10033-7","url":null,"abstract":"<p>We study pairs of symmetrically coupled, identical Lengyel-Epstein oscillators, where the coupling can be through both the fast and slow variables. We find a plethora of strong symmetry breaking rhythms, in which the two oscillators exhibit qualitatively different oscillations, and their amplitudes differ by as much as an order of magnitude. Analysis of the folded singularities in the coupled system shows that a key folded node, located off the symmetry axis, is the primary mechanism responsible for the strong symmetry breaking. Passage through the neighborhood of this folded node can result in splitting between the amplitudes of the oscillators, in which one is constrained to remain of small amplitude, while the other makes a large-amplitude oscillation or a mixed-mode oscillation. The analysis also reveals an organizing center in parameter space, where the system undergoes an asymmetric canard explosion, in which one oscillator exhibits a sequence of limit cycle canards, over an interval of parameter values centered at the explosion point, while the other oscillator executes small amplitude oscillations. Other folded singularities can also impact properties of the strong symmetry breaking rhythms. We contrast these strong symmetry breaking rhythms with asymmetric rhythms that are close to symmetric states, such as in-phase or anti-phase oscillations. In addition to the symmetry breaking rhythms, we also find an explosion of anti-phase limit cycle canards, which mediates the transition from small-amplitude, anti-phase oscillations to large-amplitude, anti-phase oscillations.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576021","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":"Dynamics of a Piecewise-Linear Morris–Lecar Model: Bifurcations and Spike Adding","authors":"J. Penalva, M. Desroches, A. E. Teruel, C. Vich","doi":"10.1007/s00332-024-10029-3","DOIUrl":"https://doi.org/10.1007/s00332-024-10029-3","url":null,"abstract":"<p>Multiple-timescale systems often display intricate dynamics, yet of great mathematical interest and well suited to model real-world phenomena such as bursting oscillations. In the present work, we construct a piecewise-linear version of the Morris–Lecar neuron model, denoted PWL-ML, and we thoroughly analyse its bifurcation structure with respect to three main parameters. Then, focusing on the homoclinic connection present in our PWL-ML, we study the slow passage through this connection when augmenting the original system with a slow dynamics for one of the parameters, thereby establishing a simplified framework for this slow-passage phenomenon. Our results show that our model exhibits equivalent behaviours to its smooth counterpart. In particular, we identify canard solutions that are part of spike-adding transitions. Focusing on the one-spike and on the two-spike scenarios, we prove their existence in a more straightforward manner than in the smooth context. In doing so, we present several techniques that are specific to the piecewise-linear framework and with the potential to offer new tools for proving the existence of dynamical objects in a wider context.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575856","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":"Existence, Stability and Slow Dynamics of Spikes in a 1D Minimal Keller–Segel Model with Logistic Growth","authors":"Fanze Kong, Michael J. Ward, Juncheng Wei","doi":"10.1007/s00332-024-10025-7","DOIUrl":"https://doi.org/10.1007/s00332-024-10025-7","url":null,"abstract":"<p>We analyze the existence, linear stability, and slow dynamics of localized 1D spike patterns for a Keller–Segel model of chemotaxis that includes the effect of logistic growth of the cellular population. Our analysis of localized patterns for this two-component reaction–diffusion (RD) model is based, not on the usual limit of a large chemotactic drift coefficient, but instead on the singular limit of an asymptotically small diffusivity <span>(d_2=epsilon ^2ll 1)</span> of the chemoattractant concentration field. In the limit <span>(d_2ll 1)</span>, steady-state and quasi-equilibrium 1D multi-spike patterns are constructed asymptotically. To determine the linear stability of steady-state <i>N</i>-spike patterns, we analyze the spectral properties associated with both the “large” <span>({{mathcal {O}}}(1))</span> and the “small” <i>o</i>(1) eigenvalues associated with the linearization of the Keller–Segel model. By analyzing a nonlocal eigenvalue problem characterizing the large eigenvalues, it is shown that <i>N</i>-spike equilibria can be destabilized by a zero-eigenvalue crossing leading to a competition instability if the cellular diffusion rate <span>(d_1)</span> exceeds a threshold, or from a Hopf bifurcation if a relaxation time constant <span>(tau )</span> is too large. In addition, a matrix eigenvalue problem that governs the stability properties of an <i>N</i>-spike steady-state with respect to the small eigenvalues is derived. From an analysis of this matrix problem, an explicit range of <span>(d_1)</span> where the <i>N</i>-spike steady-state is stable to the small eigenvalues is identified. Finally, for quasi-equilibrium spike patterns that are stable on an <span>({{mathcal {O}}}(1))</span> time-scale, we derive a differential algebraic system (DAE) governing the slow dynamics of a collection of localized spikes. Unexpectedly, our analysis of the KS model with logistic growth in the singular limit <span>(d_2ll 1)</span> is rather closely related to the analysis of spike patterns for the Gierer–Meinhardt RD system.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575779","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":"Environmental Stochasticity Driving the Extinction of Top Predators in a Food Chain Chemostat Model","authors":"Anji Yang, Sanling Yuan, Tonghua Zhang","doi":"10.1007/s00332-024-10026-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10026-6","url":null,"abstract":"<p>Understanding the process of extinction in natural populations is crucial for the preservation of ecosystem stability and biodiversity, both theoretically and practically. The risk of extinction in these populations is often influenced by environmental stochasticity, which has a significant impact on birth and mortality rates. In this study, we propose a tri-trophic food chain model that incorporates random disturbances in the environment, represented by a chemostat, which is an ideal mathematical model for simulating diverse ecosystems. In the absence of noise, the model exhibits two types of bistability, indicating that the stochastic system has two distinct paths to extinction: from a stationary state or from an oscillatory state. For each type, we determine the tipping value of environmental stochasticity that leads to the extinction of top predators by constructing confidence regions for the corresponding coexisting attractor. Furthermore, we observe a high skewness and heavy-tailed distribution of extinction times for intermediate and high levels of environmental stochasticity, consistent with empirical data. To analyze extinction times, we employ the Lévy distribution, a statistical model that describes power-law tail distributions. Our findings demonstrate that, for a fixed dilution rate, increasing environmental stochasticity reduces the average extinction time, thereby accelerating species extinction. Additionally, for a certain level of stochasticity, the average extinction time decreases with the magnitude of the dilution rate due to the heavy-tailed nature of the extinction time distribution.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575945","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":"Nonlinear Feedback, Double-bracket Dissipation and Port Control of Lie–Poisson Systems","authors":"Simon Hochgerner","doi":"10.1007/s00332-024-10031-9","DOIUrl":"https://doi.org/10.1007/s00332-024-10031-9","url":null,"abstract":"<p>Methods from controlled Lagrangians, double-bracket dissipation and interconnection and damping assignment–passivity-based control (IDA-PBC) are used to construct nonlinear feedback controls which (asymptotically) stabilize previously unstable equilibria of Lie–Poisson Hamiltonian systems. The results are applied to find an asymptotically stabilizing control for the rotor driven satellite, and a stabilizing control for Hall magnetohydrodynamic flow.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576233","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":"Multiple Higher-Order Pole Solutions in Spinor Bose–Einstein Condensates","authors":"","doi":"10.1007/s00332-024-10024-8","DOIUrl":"https://doi.org/10.1007/s00332-024-10024-8","url":null,"abstract":"<h3>Abstract</h3> <p>In this study, multiple higher-order pole solutions of spinor Bose–Einstein condensates are explored by means of the inverse scattering transform, which are associated with different higher-order pole pairs of the transmission coefficient and give solutions to the spin-1 Gross–Pitaevskii equation. First, a direct scattering problem is introduced to map the initial data to the scattering data, which includes discrete spectrums, reflection coefficients, and a polynomial that replaces the normalized constants. In order to analyze symmetries and discrete spectra in the direct scattering problem, a generalized cross product is defined in four-dimensional vector Space. The inverse scattering problem is then characterized in terms of the <span> <span>(4times 4)</span> </span> matrix Riemann–Hilbert problem that is subject to the residual conditions of these higher-order poles. In the reflectionless case, the Riemann–Hilbert problem can be converted into a linear algebraic system, which has a unique solution and allows us to explicitly obtain multiple higher-order pole solutions to the spin-1 Gross–Pitaevskii equation. </p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140575852","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":"Modeling the p53-Mdm2 Dynamics Triggered by DNA Damage","authors":"Zirui Zhu, Yancong Xu, Xingbo Liu, Shigui Ruan","doi":"10.1007/s00332-024-10023-9","DOIUrl":"https://doi.org/10.1007/s00332-024-10023-9","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140358404","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}