Journal of Nonlinear Science最新文献

Biologically Inspired Pectoral Propulsors with Flapping and Rowing Control for a Specified Stroke Plane Angle 具有特定冲程平面角度的拍打和划船控制功能的生物启发胸桨

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-17 DOI: 10.1007/s00332-024-10078-8

Bing Luo, Wei Li

{"title":"Biologically Inspired Pectoral Propulsors with Flapping and Rowing Control for a Specified Stroke Plane Angle","authors":"Bing Luo, Wei Li","doi":"10.1007/s00332-024-10078-8","DOIUrl":"https://doi.org/10.1007/s00332-024-10078-8","url":null,"abstract":"Many flying and swimming creatures have morphing pectoral propulsors (wings or fins) for propulsion, typically with flapping, rowing, and pitching motions; flapping and rowing motions are responsible for the stroke plane angle that is important for a broader performance space of the propulsor, while the stroke plane angle has been less characterized and implemented by artificial propulsors of biomimetic vehicles and thus has lack of stroke plane angle control. In this paper, we consider robotic pectoral propulsors with combined flapping and rowing motions for a stroke plane angle that can be generally specified. We consider two possible rotation axes configurations (i.e., the dependence of the rotation axes for flapping and rowing). For each rotation axes configuration, we propose the kinematic relations between the flapping and rowing motions for a generally specified stroke plane angle and provide the general flapping (or rowing) kinematics as a function of the rowing (or flapping) kinematics, which have not been characterized previously. These results serve as the reference trajectories of the propulsor for specified stroke plane angles and have implications for stroke plane angle control and thus have implications to achieve a broader performance space for biomimetic propulsors.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"77 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269337","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}

引用次数: 0

Critical Transitions for Asymptotically Concave or d-Concave Nonautonomous Differential Equations with Applications in Ecology 渐近凹或 d-Concave 非自治微分方程的临界转换及其在生态学中的应用

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-16 DOI: 10.1007/s00332-024-10088-6

Jesús Dueñas, Carmen Núñez, Rafael Obaya

{"title":"Critical Transitions for Asymptotically Concave or d-Concave Nonautonomous Differential Equations with Applications in Ecology","authors":"Jesús Dueñas, Carmen Núñez, Rafael Obaya","doi":"10.1007/s00332-024-10088-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10088-6","url":null,"abstract":"The occurrence of tracking or tipping situations for a transition equation (x'=f(t,x,Gamma (t,x))) with asymptotic limits (x'=f(t,x,Gamma _pm (t,x))) is analyzed. The approaching condition is just (lim _{trightarrow pm infty }(Gamma (t,x)-Gamma _pm (t,x))=0) uniformly on compact real sets, and so there is no restriction to the dependence on time of the asymptotic equations. The hypotheses assume concavity in x either of the maps (xmapsto f(t,x,Gamma _pm (t,x))) or of their derivatives with respect to the state variable (d-concavity), but not of (xmapsto f(t,x,Gamma (t,x))) nor of its derivative. The analysis provides a powerful tool to analyze the occurrence of critical transitions for one-parametric families (x'=f(t,x,Gamma ^c(t,x))). The new approach significatively widens the field of application of the results, since the evolution law of the transition equation can be essentially different from those of the limit equations. Among these applications, some scalar population dynamics models subject to nontrivial predation and migration patterns are analyzed, both theoretically and numerically. Some key points in the proofs are: to understand the transition equation as part of an orbit in its hull which approaches the -limit and <img alt=\"\" src=\"//media.springernature.com/lw17/springer-static/image/art%3A10.1007%2Fs00332-024-10088-6/MediaObjects/332_2024_10088_IEq8_HTML.gif\" style=\"width:17px;max-width:none;\"/>-limit sets; to observe that these sets concentrate all the ergodic measures; and to prove that in order to describe the dynamical possibilities of the equation it is sufficient that the concavity or d-concavity conditions hold for a complete measure subset of the equations of the hull.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"77 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142257205","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}

引用次数: 0

A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves 共振李亚普诺夫中心定理在双周期水弹性游波中的应用

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-14 DOI: 10.1007/s00332-024-10073-z

R. Ahmad, M. D. Groves, D. Nilsson

{"title":"A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves","authors":"R. Ahmad, M. D. Groves, D. Nilsson","doi":"10.1007/s00332-024-10073-z","DOIUrl":"https://doi.org/10.1007/s00332-024-10073-z","url":null,"abstract":"We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or (1:-1) semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or (1:-1) semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"18 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142257206","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}

引用次数: 0

Solitary-Wave Solutions of the Fractional Nonlinear Schrödinger Equation: I—Existence and Numerical Generation 分数非线性薛定谔方程的孤波解：I-存在性与数值生成

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-11 DOI: 10.1007/s00332-024-10086-8

Angel Durán, Nuria Reguera

引用次数: 0

Chaotic Dynamics at the Boundary of a Basin of Attraction via Non-transversal Intersections for a Non-global Smooth Diffeomorphism 通过非全局光滑衍射的非横向交叉在吸引盆地边界的混沌动力学

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-11 DOI: 10.1007/s00332-024-10079-7

Ernest Fontich, Antonio Garijo, Xavier Jarque

引用次数: 0

Stability and Bifurcation Analysis of a Reaction–Diffusion SIRS Epidemic Model with the General Saturated Incidence Rate 具有一般饱和发病率的反应-扩散 SIRS 流行模型的稳定性和分岔分析

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-04 DOI: 10.1007/s00332-024-10081-z

Gaoyang She, Fengqi Yi

{"title":"Stability and Bifurcation Analysis of a Reaction–Diffusion SIRS Epidemic Model with the General Saturated Incidence Rate","authors":"Gaoyang She, Fengqi Yi","doi":"10.1007/s00332-024-10081-z","DOIUrl":"https://doi.org/10.1007/s00332-024-10081-z","url":null,"abstract":"In this paper, we are concerned with the dynamics of a reaction–diffusion SIRS epidemic model with the general saturated nonlinear incidence rates. Firstly, we show the global existence and boundedness of the in-time solutions for the parabolic system. Secondly, for the ODEs system, we analyze the existence and stability of the disease-free equilibrium solution, the endemic equilibrium solutions as well as the bifurcating periodic solution. In particular, in the language of the basic reproduction number, we are able to address the existence of the saddle-node-like bifurcation and the secondary bifurcation (Hopf bifurcation). Our results also suggest that the ODEs system has a Allee effect, i.e., one can expect either the coexistence of a stable disease-free equilibrium and a stable endemic equilibrium solution, or the coexistence of a stable disease-free equilibrium solution and a stable periodic solution. Finally, for the PDEs system, we are capable of deriving the Turing instability criteria in terms of the diffusion rates for both the endemic equilibrium solutions and the Hopf bifurcating periodic solution. The onset of Turing instability can bring out multi-level bifurcations and manifest itself as the appearance of new spatiotemporal patterns. It seems also interesting to note that p and k, appearing in the saturated incidence rate (kSI^p/(1+alpha I^p)), tend to play far reaching roles in the spatiotemporal pattern formations.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"185 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206262","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}

引用次数: 0

Measure-Valued Structured Deformations 量值结构变形

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-03 DOI: 10.1007/s00332-024-10076-w

Stefan Krömer, Martin Kružík, Marco Morandotti, Elvira Zappale

引用次数: 0

The Dynamics of Periodic Traveling Interfacial Electrohydrodynamic Waves: Bifurcation and Secondary Bifurcation 周期性行进的界面电流体动力波的动力学：分岔和二次分岔

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-09-02 DOI: 10.1007/s00332-024-10085-9

Guowei Dai, Fei Xu, Yong Zhang

引用次数: 0

Integrable Variants of the Toda Lattice 户田格子的可积分变体

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-08-29 DOI: 10.1007/s00332-024-10072-0

Ya-Jie Liu, Hui Alan Wang, Xiang-Ke Chang, Xing-Biao Hu, Ying-Nan Zhang

{"title":"Integrable Variants of the Toda Lattice","authors":"Ya-Jie Liu, Hui Alan Wang, Xiang-Ke Chang, Xing-Biao Hu, Ying-Nan Zhang","doi":"10.1007/s00332-024-10072-0","DOIUrl":"https://doi.org/10.1007/s00332-024-10072-0","url":null,"abstract":"By introducing bilinear operators of trigonometric type, we propose several novel integrable variants of the famous Toda lattice, two of which can be regarded as integrable discretizations of the Kadomtsev–Petviashvili equation—a universal model describing weakly nonlinear waves in media with dispersion of velocity. We also demonstrate that two one-dimensional reductions of these variants can approximate the nonlinear Schrödinger equation and a generalized nonlinear Schrödinger equation well. It turns out that these equations admit meaningful solutions including solitons, breathers, lumps and rogue waves, which are expressed in terms of explicit and closed forms. In particular, it seems to be the first time that rogue wave solutions have been obtained for Toda-type equations. Furthermore, g-periodic wave solutions are also produced in terms of Riemann theta function. An approximation solution of the three-periodic wave is successfully carried out by using a deep neural network. The introduction of trigonometric-type bilinear operators is also efficient in generating new variants together with rich properties for some other integrable equations.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"71 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206281","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}

引用次数: 0

Finite-Time Analysis of Crises in a Chaotically Forced Ocean Model 混沌强迫海洋模型危机的有限时间分析

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-08-28 DOI: 10.1007/s00332-024-10077-9

Andrew R. Axelsen, Courtney R. Quinn, Andrew P. Bassom

{"title":"Finite-Time Analysis of Crises in a Chaotically Forced Ocean Model","authors":"Andrew R. Axelsen, Courtney R. Quinn, Andrew P. Bassom","doi":"10.1007/s00332-024-10077-9","DOIUrl":"https://doi.org/10.1007/s00332-024-10077-9","url":null,"abstract":"We consider a coupling of the Stommel box model and the Lorenz model, with the goal of investigating the so-called crises that are known to occur given sufficient forcing. In this context, a crisis is characterized as the destruction of a chaotic attractor under a critical forcing strength. We document the variety of chaotic attractors and crises possible in our model, focusing on the parameter region where the Lorenz model is always chaotic and where bistability exists in the Stommel box model. The chaotic saddle collisions that occur in a boundary crisis are visualized, with the chaotic saddle computed using the Saddle-Straddle Algorithm. We identify a novel sub-type of boundary crisis, namely a vanishing basin crisis. For forcing strength beyond the crisis, we demonstrate the possibility of a merging between the persisting chaotic attractor and either a chaotic transient or a ghost attractor depending on the type of boundary crisis. An investigation of the finite-time Lyapunov exponents around crisis levels of forcing reveals a convergence between two near-neutral exponents, particularly at points of a trajectory most sensitive to divergence. This points to loss of hyperbolicity associated with crisis occurrence. Finally, we generalize our findings by coupling the Stommel box model to other strange attractors and thereby show that the behaviors are quite generic and robust.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"185 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226303","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}

引用次数: 0