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Physica D: Nonlinear Phenomena最新文献

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Jensen-autocorrelation function for weakly stationary processes and applications 弱静止过程的詹森自相关函数及其应用
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-11-07 DOI: 10.1016/j.physd.2024.134424
Javier E. Contreras-Reyes
{"title":"Jensen-autocorrelation function for weakly stationary processes and applications","authors":"Javier E. Contreras-Reyes","doi":"10.1016/j.physd.2024.134424","DOIUrl":"10.1016/j.physd.2024.134424","url":null,"abstract":"<div><div>The Jensen-variance (JV) information based on Jensen’s inequality and variance has been previously proposed to measure the distance between two random variables. Based on the relationship between JV distance and autocorrelation function of two weakly stationary process, the Jensen-autocovariance and Jensen-autocorrelation functions are proposed in this paper. Furthermore, the distance between two different weakly stationary processes is measured by the Jensen-cross-correlation function. Moreover, autocorrelation function is also considered for ARMA and ARFIMA processes, deriving explicit formulas for Jensen-autocorrelation function that only depends on model parametric space and lag, whose were also illustrated by numeric results. In order to study the usefulness of proposed functions, two real-life applications were considered: the Tree Ring and Southern Humboldt current ecosystem time series.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134424"},"PeriodicalIF":2.7,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654563","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}
引用次数: 0
About the chaos influence on a system with multi-frequency quasi-periodicity and the Landau-Hopf scenario 关于混沌对多频准周期性系统的影响以及 Landau-Hopf 情景
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-11-06 DOI: 10.1016/j.physd.2024.134425
A.P. Kuznetsov, L.V. Turukina
{"title":"About the chaos influence on a system with multi-frequency quasi-periodicity and the Landau-Hopf scenario","authors":"A.P. Kuznetsov,&nbsp;L.V. Turukina","doi":"10.1016/j.physd.2024.134425","DOIUrl":"10.1016/j.physd.2024.134425","url":null,"abstract":"<div><div>The interaction of system demonstrating multi-frequency quasi-periodic oscillations and several steps of the Landau-Hopf scenario with chaotic Rössler system is considered. The quasi-periodic subsystem is a network of five non-identical van der Pol oscillators. It is shown that as the coupling parameter between the subsystems decreases, successive quasi-periodic Hopf bifurcations and doublings of high-dimensional invariant tori are observed. The chaos arising in this system can have several (in our case up to five) additional zero Lyapunov exponents. In case of weak coupling parameter between chaotic and quasi-periodic subsystems, when the coupling parameter of van der Pol oscillators changes, the points at which the attractor transformation occurs are observed. This is a new type of bifurcations that are responsible for a consistent increase in the number of additional zero Lyapunov exponents. As the coupling parameter between chaotic and quasi-periodic subsystems increases, the observed stages of the Landau-Hopf scenario turns out to be resistant to interaction with the chaotic system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134425"},"PeriodicalIF":2.7,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661130","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}
引用次数: 0
Soliton resolution for the Ostrovsky–Vakhnenko equation 奥斯特洛夫斯基-瓦赫年科方程的孤子解析
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134416
Ruihong Ma, Engui Fan
{"title":"Soliton resolution for the Ostrovsky–Vakhnenko equation","authors":"Ruihong Ma,&nbsp;Engui Fan","doi":"10.1016/j.physd.2024.134416","DOIUrl":"10.1016/j.physd.2024.134416","url":null,"abstract":"<div><div>We consider the Cauchy problem of the Ostrovsky–Vakhnenko (OV) equation expressed in the new variables <span><math><mrow><mo>(</mo><mi>y</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span> <span><span><span><math><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>−</mo><mi>q</mi><msub><mrow><mrow><mo>(</mo><mo>log</mo><mi>q</mi><mo>)</mo></mrow></mrow><mrow><mi>y</mi><mi>τ</mi></mrow></msub><mo>−</mo><mn>1</mn><mo>=</mo><mn>0</mn></mrow></math></span></span></span> with Schwartz initial data <span><math><mrow><msub><mrow><mi>q</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>&gt;</mo><mn>0</mn></mrow></math></span> which supports smooth and single-valued solitons. It is shown that the solution to the Cauchy problem for the OV equation can be characterized by a 3 × 3 matrix Riemann–Hilbert (RH) problem. Furthermore, by employing the <span><math><mover><mrow><mi>∂</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span>-steepest descent method to deform the RH problem into solvable models, we derive the soliton resolution for the OV equation across two space–time regions: <span><math><mrow><mi>y</mi><mo>/</mo><mi>τ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>y</mi><mo>/</mo><mi>τ</mi><mo>&lt;</mo><mn>0</mn></mrow></math></span>. This result also implies that the <span><math><mi>N</mi></math></span>-soliton solutions of the OV equation in variables <span><math><mrow><mo>(</mo><mi>y</mi><mo>,</mo><mi>τ</mi><mo>)</mo></mrow></math></span> are asymptotically stable.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134416"},"PeriodicalIF":2.7,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654424","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}
引用次数: 0
Global dynamics of a periodically forced SI disease model of Lotka–Volterra type 洛特卡-沃尔特拉型周期性强迫 SI 疾病模型的全局动力学
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134422
Yuheng Song , Lei Niu
{"title":"Global dynamics of a periodically forced SI disease model of Lotka–Volterra type","authors":"Yuheng Song ,&nbsp;Lei Niu","doi":"10.1016/j.physd.2024.134422","DOIUrl":"10.1016/j.physd.2024.134422","url":null,"abstract":"<div><div>In this paper, we investigate the dynamics of an SI disease model of Lotka–Volterra type in the presence of a periodically fluctuating environment. We give a global analysis of the dynamical behavior of the model. Interestingly, our results show that the permanence guarantees the existence of a unique positive harmonic time-periodic solution which is globally attracting when the horizontal disease transmission has a weaker impact than the intraspecific competition. While for the case when the horizontal disease transmission has a stronger impact than the intraspecific competition, we numerically show that complex dynamics such as chaos can occur in a permanent system. Nonetheless, we provide sufficient conditions for the existence and uniqueness of the positive harmonic time-periodic solution for the latter case. The impact of the environment on the spread of disease is studied by using a bifurcation analysis. We show that in each of the qualitatively different cases of the associated autonomous SI model in a constant environment, an alternative possibility can appear in the periodic model.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134422"},"PeriodicalIF":2.7,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654369","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}
引用次数: 0
Chaotic fields out of equilibrium are observable independent 失去平衡的混沌场是独立可观测的
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134421
D. Lippolis
{"title":"Chaotic fields out of equilibrium are observable independent","authors":"D. Lippolis","doi":"10.1016/j.physd.2024.134421","DOIUrl":"10.1016/j.physd.2024.134421","url":null,"abstract":"<div><div>Chaotic dynamics is always characterized by swarms of unstable trajectories, unpredictable individually, and thus generally studied statistically. It is often the case that such phase-space densities relax exponentially fast to a limiting distribution, that rules the long-time average of every observable of interest. Before that asymptotic time scale, the statistics of chaos is generally believed to depend on both the initial conditions and the chosen observable. I show that this is not the case for a widely applicable class of models, that feature a phase-space (‘field’) distribution common to all pushed-forward or integrated observables, while the system is still relaxing towards statistical equilibrium or a stationary state. This universal profile is determined by both leading and first subleading eigenfunctions of the transport operator (Koopman or Perron–Frobenius) that maps phase-space densities forward or backward in time.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134421"},"PeriodicalIF":2.7,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142661129","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}
引用次数: 0
Jacobi stability, Hamilton energy and the route to hidden attractors in the 3D Jerk systems with unique Lyapunov stable equilibrium 具有唯一李雅普诺夫稳定均衡的三维 Jerk 系统中的雅可比稳定性、汉密尔顿能量和通向隐藏吸引子的路径
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-11-04 DOI: 10.1016/j.physd.2024.134423
Xiaoting Lu, Qigui Yang
{"title":"Jacobi stability, Hamilton energy and the route to hidden attractors in the 3D Jerk systems with unique Lyapunov stable equilibrium","authors":"Xiaoting Lu,&nbsp;Qigui Yang","doi":"10.1016/j.physd.2024.134423","DOIUrl":"10.1016/j.physd.2024.134423","url":null,"abstract":"<div><div>This paper is devoted to reveal the generation mechanism of hidden attractors of the 3D Jerk systems with unique Lyapunov stable equilibrium. In the light of the deviation curvature tensor, the two-parameter regions with Lyapunov stable but Jacobi unstable equilibrium are identified. Within these regions, the system’s dynamics transition from Lyapunov stable but Jacobi unstable equilibrium to hidden periodic and then to hidden chaotic attractors, which the corresponding Hamilton energy tend to be constant, regular and irregular oscillations, respectively. The route to hidden attractors of the systems with Jacobi unstable equilibrium is analyzed under one parameter variation. The results show that the systems initially undergo a subcritical Hopf bifurcation, resulting in a Lyapunov unstable limit cycle, followed by a saddle–node bifurcation of limit cycle, ultimately entering hidden chaotic attractors via the Feigenbaum period-doubling route.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134423"},"PeriodicalIF":2.7,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654423","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}
引用次数: 0
Formal solutions of some family of inhomogeneous nonlinear partial differential equations, Part 2: Summability 某些非均质非线性偏微分方程族的形式解，第 2 部分：可求和性
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-11-01 DOI: 10.1016/j.physd.2024.134420
Alberto Lastra , Pascal Remy , Maria Suwińska
{"title":"Formal solutions of some family of inhomogeneous nonlinear partial differential equations, Part 2: Summability","authors":"Alberto Lastra ,&nbsp;Pascal Remy ,&nbsp;Maria Suwińska","doi":"10.1016/j.physd.2024.134420","DOIUrl":"10.1016/j.physd.2024.134420","url":null,"abstract":"<div><div>In this article, we investigate the summability of the formal power series solutions in time of a class of inhomogeneous nonlinear partial differential equations in two variables, whose corresponding Newton polygon admits a unique positive slope <span><math><mi>k</mi></math></span>, the latter being determined by the highest spatial-derivative order of the initial equation. We give in particular a necessary and sufficient condition for the <span><math><mi>k</mi></math></span>-summability of the solutions in a given direction, and we illustrate this result by some examples. This condition generalizes the ones already given by the second author in Remy (2016, 2020, 2021 [25,26], 2022, 2023). In addition, we present some technical results on the generalized binomial and multinomial coefficients, which are needed for the proof of our main result.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134420"},"PeriodicalIF":2.7,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142592647","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}
引用次数: 0
To blow-up or not to blow-up for a granular kinetic equation 颗粒动力学方程的吹胀与否
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-10-28 DOI: 10.1016/j.physd.2024.134410
José A. Carrillo , Ruiwen Shu , Li Wang , Wuzhe Xu
{"title":"To blow-up or not to blow-up for a granular kinetic equation","authors":"José A. Carrillo ,&nbsp;Ruiwen Shu ,&nbsp;Li Wang ,&nbsp;Wuzhe Xu","doi":"10.1016/j.physd.2024.134410","DOIUrl":"10.1016/j.physd.2024.134410","url":null,"abstract":"<div><div>A simplified kinetic description of rapid granular media leads to a nonlocal Vlasov-type equation with a convolution integral operator that is of the same form as the continuity equations for aggregation-diffusion macroscopic dynamics. While the singular behavior of these nonlinear continuity equations is well studied in the literature, the extension to the corresponding granular kinetic equation is highly nontrivial. The main question is whether the singularity formed in velocity direction will be enhanced or mitigated by the shear in phase space due to free transport. We present a preliminary study through a meticulous numerical investigation and heuristic arguments. We have numerically developed a structure-preserving method with adaptive mesh refinement that can effectively capture potential blow-up behavior in the solution for granular kinetic equations. We have analytically constructed a finite-time blow-up infinite mass solution and discussed how this can provide insights into the finite mass scenario.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134410"},"PeriodicalIF":2.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142654368","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}
引用次数: 0
Conservative deep neural networks for modeling competition of ribosomes with extended length 保守型深度神经网络为加长核糖体的竞争建模
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-10-28 DOI: 10.1016/j.physd.2024.134415
Naman Krishna Pande, Aditi Jain, Arun Kumar, Arvind Kumar Gupta
{"title":"Conservative deep neural networks for modeling competition of ribosomes with extended length","authors":"Naman Krishna Pande,&nbsp;Aditi Jain,&nbsp;Arun Kumar,&nbsp;Arvind Kumar Gupta","doi":"10.1016/j.physd.2024.134415","DOIUrl":"10.1016/j.physd.2024.134415","url":null,"abstract":"<div><div>We develop a network model that combines several ribosome flow models with extended objects (RFMEO) competing for the finite pool of ribosomes. This alleviates the need to systematically coarse-grain the mRNA molecules. The dynamics of the network is described by a system of non-linear ordinary differential equations. It is shown that the network always converges to a steady state for a fixed number of ribosomes. Our analysis shows that increasing any of the transition rates along an RFMEO increases its output rate and either the output rates of the other RFMEOs all increase or all decrease. Simulations also demonstrate a counterintuitive result that increasing the ribosomal footprint may sometimes lead to an increase in the network production rate. Next, we propose a conservative deep neural network (CDNN) framework to approximate the solution of the network. The proposed loss function also incorporates the term satisfying the first integral property of the network. Point-wise comparison of the solutions by CDNN is in good agreement with the Runge–Kutta based numerical solution. Also, the CDNN framework offers a closed-form solution of the RFMEONP as a function of free parameters, thus allowing evaluation of the solution at any parameter value without again simulating the system.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134415"},"PeriodicalIF":2.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142573440","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}
引用次数: 0
On the blow-up for a Kuramoto–Velarde type equation 论 Kuramoto-Velarde 型方程的炸毁问题
IF 2.7 3区 数学
Physica D: Nonlinear Phenomena Pub Date : 2024-10-24 DOI: 10.1016/j.physd.2024.134407
Oscar Jarrín , Gaston Vergara-Hermosilla
{"title":"On the blow-up for a Kuramoto–Velarde type equation","authors":"Oscar Jarrín ,&nbsp;Gaston Vergara-Hermosilla","doi":"10.1016/j.physd.2024.134407","DOIUrl":"10.1016/j.physd.2024.134407","url":null,"abstract":"<div><div>It is known that the Kuramoto–Velarde equation is globally well-posed on Sobolev spaces in the case when the parameters <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> involved in the non-linear terms verify <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span> or <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0</mn></mrow></math></span>. In the complementary case of these parameters, the global existence or blow-up of solutions is a completely open (and hard) problem. Motivated by this fact, in this work we consider a non-local version of the Kuramoto–Velarde equation. This equation allows us to apply a Fourier-based method and, within the framework <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≠</mo><mfrac><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span> and <span><math><mrow><msub><mrow><mi>γ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>≠</mo><mn>0</mn></mrow></math></span>, we show that large values of these parameters yield a blow-up in finite time of solutions in the Sobolev norm. As a complement to it, we address an alternative result on the finite-time blow-up of smooth solutions by considering a <em>virial</em>-type estimate.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134407"},"PeriodicalIF":2.7,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552521","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}
引用次数: 0
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