Journal of Nonlinear Science最新文献

{"title":"Well-Posedness and Stability Analysis of a Landscape Evolution Model","authors":"Julie Binard, Pierre Degond, Pascal Noble","doi":"10.1007/s00332-023-09997-9","DOIUrl":"https://doi.org/10.1007/s00332-023-09997-9","url":null,"abstract":"<p>In this paper, we study a system of partial differential equations modeling the evolution of a landscape in order to describe the mechanisms of pattern formations. A ground surface is eroded by the flow of water over it, by either sedimentation or dilution. We consider a model, composed of three evolution equations: one on the elevation of the ground surface, one on the fluid height and one on the concentration of sediments in the fluid layer. We first establish the well-posedness of the system in short time and under the assumption that the initial fluid height does not vanish. Then, we focus on pattern formation in the case of a film flow over an inclined erodible plane. For that purpose, we carry out a spectral stability analysis of constant state solutions in order to determine instability conditions and identify a mechanism for pattern formations. These patterns, which are rills and gullies, are the starting point of the formation of rivers and valleys in landscapes. Finally, we carry out some numerical simulations of the full system in order to validate the spectral instability scenario, and determine the resulting patterns.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"103 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518645","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":"Cognitive Consumer-Resource Spatiotemporal Dynamics with Nonlocal Perception","authors":"Yongli Song, Hao Wang, Jinfeng Wang","doi":"10.1007/s00332-023-09996-w","DOIUrl":"https://doi.org/10.1007/s00332-023-09996-w","url":null,"abstract":"<p>Nonlocal perception is crucial to the mechanistic modeling of cognitive animal movement. We formulate a diffusive consumer-resource model with nonlocal perception on resource availability, where resource dynamics is explicitly modeled, to investigate the influence of nonlocal perception on stability and spatiotemporal patterns. For the finite domain, nonlocal perception described by two common types of resource detection function (spatial average or Green function) has no impact on the stability of the spatially homogeneous steady state. For the infinite domain, nonlocal perception described by the Laplacian or Gaussian detection function has no impact on stability either; however, the top-hat detection function can destabilize the spatially homogeneous steady state when the rate of perceptual movement is large and the detection scale belongs to an appropriate interval. Using the more realistic top-hat perception kernel, we investigate the influence of the detection scale, the perceptual movement rate and the resource’s carrying capacity on the spatiotemporal patterns and find the stripe spatial patterns, oscillatory patterns with different spatial profiles as well as spatiotemporal chaos.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"138 ","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518648","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":"Oscillations in a Fully Connected Network of Leaky Integrate-and-Fire Neurons with a Poisson Spiking Mechanism","authors":"Grégory Dumont, Jacques Henry, Carmen Oana Tarniceriu","doi":"10.1007/s00332-023-09995-x","DOIUrl":"https://doi.org/10.1007/s00332-023-09995-x","url":null,"abstract":"<p>Understanding the mechanisms that lead to oscillatory activity in the brain is an ongoing challenge in computational neuroscience. Here, we address this issue by considering a network of excitatory neurons with Poisson spiking mechanism. In the mean-field formalism, the network’s dynamics can be successfully rendered by a nonlinear dynamical system. The stationary state of the system is computed and a perturbation analysis is performed to obtain an analytical characterization for the occurrence of instabilities. Taking into account two parameters of the neural network, namely synaptic coupling and synaptic delay, we obtain numerically the bifurcation line separating the non-oscillatory from the oscillatory regime. Moreover, our approach can be adapted to incorporate multiple interacting populations.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"143 ","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518647","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":"Geometric Blow-Up for Folded Limit Cycle Manifolds in Three Time-Scale Systems","authors":"S. Jelbart, C. Kuehn, S.-V. Kuntz","doi":"10.1007/s00332-023-09987-x","DOIUrl":"https://doi.org/10.1007/s00332-023-09987-x","url":null,"abstract":"<p><i>Geometric singular perturbation theory</i> provides a powerful mathematical framework for the analysis of ‘stationary’ multiple time-scale systems which possess a <i>critical manifold</i>, i.e. a smooth manifold of steady states for the limiting fast subsystem, particularly when combined with a method of desingularisation known as <i>blow-up</i>. The theory for ‘oscillatory’ multiple time-scale systems which possess a limit cycle manifold instead of (or in addition to) a critical manifold is less developed, particularly in the non-normally hyperbolic regime. We use the blow-up method to analyse the global oscillatory transition near a regular folded limit cycle manifold in a class of three time-scale ‘semi-oscillatory’ systems with two small parameters. The systems considered behave like oscillatory systems as the smallest perturbation parameter tends to zero, and stationary systems as both perturbation parameters tend to zero. The additional time-scale structure is crucial for the applicability of the blow-up method, which cannot be applied directly to the two time-scale oscillatory counterpart of the problem. Our methods allow us to describe the asymptotics and strong contractivity of all solutions which traverse a neighbourhood of the global singularity. Our main results cover a range of different cases with respect to the relative time-scale of the angular dynamics and the parameter drift. We demonstrate the applicability of our results for systems with periodic forcing in the slow equation, in particular for a class of Liénard equations. Finally, we consider a toy model used to study tipping phenomena in climate systems with periodic forcing in the fast equation, which violates the conditions of our main results, in order to demonstrate the applicability of classical (two time-scale) theory for problems of this kind.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"21 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138518656","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":"Stochastic Gradient Descent with Noise of Machine Learning Type Part II: Continuous Time Analysis","authors":"Stephan Wojtowytsch","doi":"10.1007/s00332-023-09992-0","DOIUrl":"https://doi.org/10.1007/s00332-023-09992-0","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136227753","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":"Phase-Locked Solutions of a Coupled Pair of Nonidentical Oscillators","authors":"Kuan-Wei Chen, Chih-Wen Shih","doi":"10.1007/s00332-023-09989-9","DOIUrl":"https://doi.org/10.1007/s00332-023-09989-9","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"21 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135041699","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":"Phase-Amplitude Coordinate-Based Neural Networks for Inferring Oscillatory Dynamics","authors":"Talha Ahmed, Dan Wilson","doi":"10.1007/s00332-023-09994-y","DOIUrl":"https://doi.org/10.1007/s00332-023-09994-y","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"12 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135042849","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 Nonlocal Reaction-Diffusion Model of West Nile Virus with Vertical Transmission","authors":"Feng-Bin Wang, Ruiwen Wu, Xiao-Qiang Zhao","doi":"10.1007/s00332-023-09985-z","DOIUrl":"https://doi.org/10.1007/s00332-023-09985-z","url":null,"abstract":"","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"42 35","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432763","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":"Accurate Computations up to Breakdown of Quasi-Periodic Attractors in the Dissipative Spin–Orbit Problem","authors":"Renato Calleja, Alessandra Celletti, Joan Gimeno, Rafael de la Llave","doi":"10.1007/s00332-023-09988-w","DOIUrl":"https://doi.org/10.1007/s00332-023-09988-w","url":null,"abstract":"Abstract We consider a Celestial Mechanics model: the spin–orbit problem with a dissipative tidal torque, which is a singular perturbation of a conservative system. The goal of this paper is to show that it is possible to maintain the accuracy and reliability of the computation of quasi-periodic attractors for parameter values extremely close to the breakdown and, therefore, it is possible to obtain information on the breakdown mechanism of these quasi-periodic attractors. The method uses at the same time numerical and rigorous improvements to provide (i) a very accurate computation of the time-1 map of the spin–orbit problem (which reduces the dimensionality of the problem); (ii) a very efficient KAM method for maps which computes the attractor and its tangent spaces (by quadratically convergent, low storage requirements, and low operation count); (iii) explicit algorithms backed by a rigorous a posteriori KAM theorem, which establishes that if the algorithm is successful and produces a small residual, then there is a true solution nearby; and (iv) guaranteed algorithms to reach arbitrarily close to the border of existence as long as there are enough computer resources. As a by-product of the accuracy that we maintain till breakdown, we study several scale-invariant observables of the tori used in the renormalization group of infinite-dimensional spaces. In contrast with previously studied simple models, the behavior at breakdown of the spin–orbit problem does not satisfy standard scaling relations which implies that the spin–orbit problem is not described by a hyperbolic fixed point of the renormalization operator.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"47 52","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432120","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":"Thin-Film Equations with Singular Potentials: An Alternative Solution to the Contact-Line Paradox","authors":"Riccardo Durastanti, Lorenzo Giacomelli","doi":"10.1007/s00332-023-09982-2","DOIUrl":"https://doi.org/10.1007/s00332-023-09982-2","url":null,"abstract":"Abstract In the regime of lubrication approximation, we look at spreading phenomena under the action of singular potentials of the form $$P(h)approx h^{1-m}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>h</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>≈</mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> as $$hrightarrow 0^+$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>→</mml:mo> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> with $$m>1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> , modeling repulsion between the liquid–gas interface and the substrate. We assume zero slippage at the contact line. Based on formal analysis arguments, we report that for any $$m>1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and any value of the speed (both positive and negative) there exists a three-parameter, hence generic, family of fronts (i.e., traveling-wave solutions with a contact line). A two-parameter family of advancing “linear-log” fronts also exists, having a logarithmically corrected linear behavior in the liquid bulk. All these fronts have finite rate of dissipation, indicating that singular potentials stand as an alternative solution to the contact-line paradox. In agreement with steady states, fronts have microscopic contact angle equal to $$pi /2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> for all $$m>1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> and finite energy for all $$m<3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo><</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . We also propose a selection criterion for the fronts, based on thermodynamically consistent contact-line conditions modeling friction at the contact line. So as contact-angle conditions do in the case of slippage models, this criterion selects a unique (up to translation) linear-log front for each positive speed. Numerical evidence suggests that, fixed the speed and the frictional coefficient, its shape depends on the spreading coefficient, with steeper fronts in partial wetting and a more prominent precursor region in dry complete wetting.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"46 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634194","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}