Physica D: Nonlinear Phenomena最新文献

英文中文

Bifurcations and Marotto’s chaos of a discrete Lotka–Volterra predator–prey model

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134524

Yanan Li , Lingling Liu , Yujiang Chen , Zhiheng Yu

This paper mainly studied the qualitative properties of a four-parameter discrete Lotka–Volterra predator–prey model. By applying polynomial algebraic theory to solve complex high-order semi-algebraic systems, and combining bifurcation theory, we provided not only the topological structure of orbits in the vicinity of each fixed point, but also the specific parameter conditions that give rise to codimension one and codimension two bifurcations of the model including transcritical, flip, Neimark–Sacker bifurcations, strong resonances of 1:2, 1:3, 1:4, and weak resonance Arnold tongue. Besides, we also discussed the chaotic behavior in the sense of Marotto of the model. Finally, employing Maple 2023 and Matlab R2019a, we conducted numerical simulations of the dynamic behavior of the model to further verify the aforementioned theoretical results.

引用次数: 0

Stable oscillations in laser-induced thermal plume/surface interaction in several molecular liquids

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134492

Sean T. Oakes , Reese W. Anderson , Alex Rapelje , M.W. Gealy , Darin J. Ulness

This study explores the dynamics of thermal plumes induced by laser heating in piperidine, 1-butanol, and 1-pentanoic acid near their liquid/air interfaces. Utilizing a collimated laser beam, cylindrical heated regions are generated, acting as sources for thermal plumes outlined by refractive index gradients due to sharp temperature changes. The interaction between these plumes and the surface introduces unique steady-state dynamics, manifesting as either stable-point dynamics or anharmonic oscillations, depending on the molecular liquid and experimental conditions. Piperidine, 1-butanol, and 1-pentanoic acid each exhibit steady-state oscillation. Methanol and ethylene glycol serve as counterexamples, having stable-point dynamics. The implications of these findings are of relevance for the fields of nonlinear dynamics and dynamical systems, providing experimental examples of limit cycles.

引用次数: 0

Numerical calculation and characteristics of quasi-periodic breathers to the Kadomtsev–Petviashvili-based system

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134497

Zhonglong Zhao, Yu Wang, Pengcheng Xin

The Kadomtsev–Petviashvili-based system can be regarded as a consistent approximation of a class of partial differential equations, which can be used to describe the nonlinear wave phenomena in the fields of ionomers, fluid dynamics and optical systems. In this paper, an effective method is introduced to study the quasi-periodic breathers of the Kadomtsev–Petviashvili-based system. Based on the Hirota’s bilinear method and the Riemann-theta function, an over-determined system about quasi-periodic breathers can be obtained. It can be integrated into a least square problem and solved by the numerical iterative algorithms. The asymptotic properties of the quasi-periodic 1-breathers are analyzed rigorously under the small amplitude limit. The dynamic behaviors including the periodicity and distance between two breather chains of the quasi-periodic breathers are analyzed precisely by an analytic method related to the characteristic lines. The effective method presented in this paper can be further extended to the other integrable systems with breathers.

引用次数: 0

Inverse scattering transform for the focusing PT-symmetric nonlinear Schrödinger equation with nonzero boundary conditions: Higher-order poles and multi-soliton solutions

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134466

Chuanxin Xu , Tao Xu , Min Li , Yehui Huang

In this paper, we extend the theory of inverse scattering transform for the focusing PT-symmetric nonlinear Schrödinger equation with nonzero boundary conditions by considering the reciprocals of scattering coefficients have multiple higher-order poles. For the inverse problem with the presence of simple, double and triple poles, we study the pole contributions, trace formulas and reconstruction formulas. On the other hand, we present the general N-soliton solutions in the determinant form for the reflectionless case, and particularly analyze the dynamics of heteroclinic multi-soliton solutions which admit the asymptotic phase difference

π

x \to \pm \infty

. It turns out that the solutions are nonsingular with a wide range of parameters and can display abundant multi-soliton interactions. The discrete eigenvalues correspond to two different localized waves: one is the conventional soliton exhibiting the dark/antidark profile, the other is the heteroclinic breather-like wave. In addition, the asymptotic solitons associated to the double- or triple-pole eigenvalues are localized in some logarithmical curves, and thus they have the variable velocities with the time dependence of attenuation.

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引用次数: 0

Consensus and bipartite consensus in graphon models for opinion dynamics on the sphere

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134503

Zhengyang Qiao, Yicheng Liu, Xiao Wang

In this article, we establish an infinite-dimensional model on the sphere for opinion dynamics based on the graph limit procedure and study consensus formation of this graphon model. Firstly, we show the existence and uniqueness of solutions for the graphon model under consideration and provide a rigorous mathematical proof of the graph limits. Then we present sufficient conditions for the emergence of consensus and bipartite consensus within our system. In the case of bipartite consensus, our results indicate that even in the absence of interactions among agents within a subgroup, they can still achieve consensus by collectively opposing the opinions of the other subgroup. Finally, we provide a series of numerical simulations to illustrate our findings.

引用次数: 0

Learning governing equations of unobserved states in dynamical systems

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134499

Gevik Grigorian , Sandip V. George , Simon Arridge

Data-driven modelling and scientific machine learning have been responsible for significant advances in determining suitable models to describe data. Within dynamical systems, neural ordinary differential equations (ODEs), where the system equations are set to be governed by a neural network, have become a popular tool for this challenge in recent years. However, less emphasis has been placed on systems that are only partially-observed. In this work, we employ a hybrid neural ODE structure, where the system equations are governed by a combination of a neural network and domain-specific knowledge, together with symbolic regression (SR), to learn governing equations of partially-observed dynamical systems. We test this approach on two case studies: A 3-dimensional model of the Lotka–Volterra system and a 5-dimensional model of the Lorenz system. We demonstrate that the method is capable of successfully learning the true underlying governing equations of unobserved states within these systems, with robustness to measurement noise.

引用次数: 0

On the compactness of the support of solitary waves of the complex saturated nonlinear Schrödinger equation and related problems

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134516

Pascal Bégout , Jesús Ildefonso Díaz

We study the vectorial stationary Schrödinger equation

- Δ u + a U + b u = F

, with a saturated nonlinearity

U = u / | u |

and with some complex coefficients

(a, b) \in ℂ^{2}

. Besides the existence and uniqueness of solutions for the Dirichlet and Neumann problems, we prove the compactness of the support of the solution, under suitable conditions on

(a, b)

and even when the source in the right hand side

F (x)

is not vanishing for large values of

| x |

. The proof of the compactness of the support uses a local energy method, given the impossibility of applying the maximum principle. We also consider the associate Schrödinger–Poisson system when coupling with a simple magnetic field. Among other consequences, our results give a rigorous proof of the existence of “solitons with compact support” claimed, without any proof, by several previous authors.

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引用次数: 0

Response analysis of vibro-impact systems under periodic and random excitations

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134476

Yahui Sun , Joseph Páez Chávez , Yang Liu , Przemysław Perlikowski

Uncertainties in factors, such as temperature, humidity, and external loads can significantly impact the performance of vibro-impact systems. Effectively managing these uncertainties is essential to ensure the reliability, safety, and performance of engineering systems in real-world operating conditions. This study presents an efficient and straightforward approach to analyze the response of vibro-impact systems subjected to both periodic and random excitations. The method estimates critical noise intensity levels that lead to dangerous noise-induced bifurcations by utilizing confidence ellipses and the global structure of the deterministic system. Furthermore, the most probable locations for stochastic attractor jumps are identified based on the evolution of the maximum eigenvalue of the stochastic sensitivity function over one period of excitation. The proposed method is validated through the analysis of both single- and two-degree-of-freedom impact oscillators. These findings provide a robust framework for predicting complex dynamic behaviors, thereby enhancing the design and application of vibro-impact systems across various engineering fields.

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引用次数: 0

Existence of dark solitons for Kundu–Eckhaus equations

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134522

Ling Pan, Shihui Zhu

This paper focuses on dark solitons and periodic solitary wave solutions for Kundu–Eckhaus equations without and with a strong generic delay, respectively. First, in terms of the dynamic system arguments, new dark solitons and periodic solitary wave solutions for the Kundu–Eckhaus equation without delay are obtained by integrating along different orbits. Then, the limits and modulation stability of the solutions of the Kundu–Eckhaus equation are investigated. Finally, the existence of two dark solitons and two periodic solitary wave solutions for Kundu–Eckhaus equations with a strong generic delays is proven via geometric singular perturbation theory.

引用次数: 0

Inverse scattering transform and the soliton solution of the discrete Ablowitz–Ladik equation

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134517

Yin Li , Meisen Chen

This paper studies the discrete Ablowitz–Ladik equation via the Riemann-Hilbert (RH) approach. By its matrix spectral problem and Lax pair, the Jost solution and the reflection coefficients are constructed. Based on the zero curvature formulation, we assume that there are higher-order zeros for the scattering coefficient

a (λ)

, and construct the corresponding RH problem. The inverse scattering transform of the discrete Ablowitz–Ladik equation is presented by the matrix spectral problem, the reconstruction formula and the RH problem, which enables us to obtain the multiple-pole solutions. And then the dynamics of one-and two-soliton solutions are discussed and presented graphically. Compared with simple-pole solutions, multiple-pole solutions possess more complicated profiles.

引用次数: 0

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