Chaos Solitons & Fractals最新文献

{"title":"Certain (2+1)-dimensional multi-soliton asymptotics in the shallow water","authors":"","doi":"10.1016/j.chaos.2024.115460","DOIUrl":"10.1016/j.chaos.2024.115460","url":null,"abstract":"<div><p>This paper investigates the Kadomtsev–Petviashvili I equation, which describes the variation of shallow-water wave amplitude in the transverse direction, making it applicable to the shallow water conditions with strong surface tension., e.g., in the capillary wave problems. With respect to the amplitude of a shallow-water-wave packet, we derive a binary Darboux transformation (DT), and then perform the asymptotic analysis on the <span><math><mi>N</mi></math></span>-soliton solutions to derive the algebraic expressions of the <span><math><mi>N</mi></math></span> soliton components, where <span><math><mi>N</mi></math></span> is a positive integer. The asymptotic results indicate the energy stability in the shallow-water soliton interactions under certain conditions. Additionally, each soliton component contributes to the phase shifts of the other soliton components. Taking <span><math><mrow><mi>N</mi><mo>=</mo><mn>3</mn></mrow></math></span> as an example, we illustrate the 3 interacting solitons via the 3D plots and density plots, which align with our asymptotic-analysis results. Although the asymptotic analysis method used is confined to the binary-DT framework, this paper tries to apply such a method [traditionally used in the <span><math><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional systems] to the aforementioned <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional system. Our analysis, which still needs to be confirmed by the relevant numerical simulation and experiments, might offer some explanations for the complex and variable natural mechanisms of the real-world shallow water waves.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ferroelectric frontiers: Navigating phase portraits, chaos, multistability and sensitivity in thin-film dynamics","authors":"","doi":"10.1016/j.chaos.2024.115540","DOIUrl":"10.1016/j.chaos.2024.115540","url":null,"abstract":"<div><p>This research includes the study of the non-linear dynamics of thin-film ferroelectric materials governed by an equation of wave dynamics within the material. This equation plays a key role in both physics and the study of aqueous flow. The work is planned as examining the symmetries group analysis drops, studying the dynamical system features through bifurcation phase portraits, and carrying dynamic phenomena in chaos theory. Diverse techniques are taken, such as Lyapunov exponent, 2D, and 3D phase portraits, Poincaré maps, time series analysis, and sensitivity to multistability under the different conditions of the initial state. In addition, the study involves using the extended hyperbolic function method to obtain the general analytical solutions via which various kinds of solitary wave solutions are produced including trigonometric and hyperbolic functions and periodic, bright, and singular soliton solutions. These solutions are followed by a list of constraint conditions in the form of equations. Visual data of 2D, 3D, and contour plots are presented, with parameters carefully set to reflect various scenarios. Sensitivity analysis is performed using alternative initial conditions, and stability analysis is demonstrated graphically. To fully grasp the dynamic features of these systems and accurately predict outcomes, it is essential to advance new technologies and methodologies that can further enhance our understanding and predictive capabilities in complex systems.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A multi-image encryption scheme based on block compressive sensing and nonlinear bifurcation diffusion","authors":"","doi":"10.1016/j.chaos.2024.115521","DOIUrl":"10.1016/j.chaos.2024.115521","url":null,"abstract":"<div><p>With the frequent cyberattacks and the rapid growth of image data volume, compressive sensing based image encryption algorithms have been widely studied. However, the existing schemes are usually imperfect in terms of encryption capacity, reconstruction quality and security. To address these issues, a novel multi-image encryption scheme is presented based on block compressive sensing and nonlinear bifurcation diffusion. Firstly, a block-level adaptive thresholding sparsification algorithm is devised to optimize the image sparsity and the decryption quality by dynamically adjusting the local thresholds for different wavelet coefficient regions according to their specific features. Secondly, to destroy the inter-block correlations while reduce the transmission burden, the orthogonal Hadamard matrix and the chaotic system are employed to construct a distinct measurement matrix for each image block. Finally, a nonlinear bifurcation diffusion algorithm based on the complete binary tree is developed to enhance the encryption performance through mutual diffusion among non-adjacent pixels. Additionally, the secure hash algorithm is employed to establish a close relation between plaintext images and secret keys to defy the chosen-plaintext attack. Simulation experiments and performance analyses demonstrate the feasibility and the reliability of our presented multi-image encryption scheme. Compared with some newly advanced schemes, our presented multi-image encryption scheme exhibits certain advantages concerning compression performance, key space, and resistance against statistical and differential attacks.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influence of an environment changing in time on crucial events: From geophysics to biology","authors":"","doi":"10.1016/j.chaos.2024.115522","DOIUrl":"10.1016/j.chaos.2024.115522","url":null,"abstract":"<div><p>This paper is devoted to the study of the interaction between two distinct forms of non-stationary processes, which we will refer to as non-stationarity of the first and second kind. The non-stationarity of the first kind is caused by criticality-generated events that we call <em>crucial events</em>. Crucial events signal ergodicity breaking emerging from the interaction between the units of the complex system under study, indicating that the non stationarity of first kind has an internal origin. The non-stationarity of second kind is due to the influence on the system of interest of an environment changing in time, thereby implying an external origin. In this paper we show that the non-stationarity of first kind, measured by an inverse power law index <span><math><mi>μ</mi></math></span> is characterized by singularities at <span><math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>μ</mi><mo>=</mo><mn>3</mn></mrow></math></span>. We realize the interaction between the non-stationarity of first kind and the non-stationarity of second kind with a model frequently adopted to study earthquakes, namely, a system of main-shocks assumed to be crucial events, generating a cascade of after-shocks simulating the changing in time environment. We prove that the after-shocks significantly affect the detection of anomalous scaling, but in the case <span><math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn></mrow></math></span>, which is sufficiently far from <span><math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>μ</mi><mo>=</mo><mn>3</mn></mrow></math></span>, both sources of singularities being strongly affected by the non-stationarity of second kind. To explain why it is possible to detect for earthquakes the value <span><math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>06</mn></mrow></math></span>, proposed in earlier work and very close to the singularity <span><math><mrow><mi>μ</mi><mo>=</mo><mn>2</mn></mrow></math></span>, we advocate a new theoretical perspective, involving a deviation from the traditional concept of criticality in physics and borrowing suggestions from biology. This new approach is based on the truncation of inverse power laws that has the effect of shifting the intermediate asymptotics to short-time region, without weakening their role for information transmission. This leads us to the conclusion that the whole planet is a living system.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243186","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pure-quartic soliton self-frequency shift in a mode-locked fiber laser","authors":"","doi":"10.1016/j.chaos.2024.115515","DOIUrl":"10.1016/j.chaos.2024.115515","url":null,"abstract":"<div><p>The pure-quartic soliton (PQS) offers the advantage of a wide spectrum and approximately Gaussian temporal profile, which has the potential to obtain high-energy ultrafast laser pulses. Thus, exploring the role of stimulated Raman scattering in the formation and propagation of PQSs in fiber lasers is crucial, especially considering the greater propensity for highpower and short PQS pulses compared to traditional solitons. Here, we present the modeling of a self-frequency shift (SFS) fiber laser based on the PQS, emphasizing the impact of fourth-order dispersion and the Raman effect. The significant red-shift in wavelength is discovered as the pump energy increases, revealing that the emergence of SFS is a universal attractor in mode-locked PQS fiber laser systems. Our simulations demonstrate that such wavelength tunability is a direct byproduct of the gain bandwidth limit and the stimulated Raman scattering for PQSs inside the fiber cavity, while the evolution dynamics in the gain and passive fiber show obvious differences. However, we find that the effect of SFS in a PQS fiber laser is compromised by a trade-off with the degradation of pulse quality, such as reshaping the oscillating tail and destroying the symmetry of the emission pulse. This Raman-induced nonlinear process under high pump energy facilitates the discovery of the comprehensive complexity of science for PQSs suffering from higher-dimensional forms of nonlinear effects in fiber lasers.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of an information theoretic analog of two masses on a spring","authors":"","doi":"10.1016/j.chaos.2024.115535","DOIUrl":"10.1016/j.chaos.2024.115535","url":null,"abstract":"<div><p>In this short communication we investigate an information theoretic analogue of the classic two masses on spring system, arising from a physical interpretation of Friston’s free energy principle in the theory of learning in a system of agents. Using methods from classical mechanics on manifolds, we define a kinetic energy term using the Fisher metric on distributions and a potential energy function defined in terms of stress on the agents’ beliefs. The resulting Lagrangian (Hamiltonian) produces a variation of the classic DeGroot dynamics. In the two agent case, the potential function is defined using the Jeffrey’s divergence and the resulting dynamics are characterized by a non-linear spring. These dynamics produce trajectories that resemble flows on tori but are shown numerically to produce chaos near the boundary of the space. We then investigate persuasion as an information theoretic control problem where analysis indicates that manipulating peer pressure with a fixed target is a more stable approach to altering an agent’s belief than providing a slowly changing belief state that approaches the target.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142243187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlinear dynamics of the semi-infinite ferromagnetic samples with an easy-plane anisotropy","authors":"","doi":"10.1016/j.chaos.2024.115500","DOIUrl":"10.1016/j.chaos.2024.115500","url":null,"abstract":"<div><p>The modification of the inverse scattering problem is proposed to investigate solitons and dispersive waves in the framework of the Landau–Lifshitz model for semi-infinite ferromagnet with an ¡¡easy-plane¿¿ anisotropy under the mixed boundary conditions, corresponding to different degrees of spin pinning on the edge of the sample. New types of solitons are obtained and their elastic reflection from the edge of the sample is analyzed. Spectral expansions of the integrals of motion for solitons and waves are found. Additional integrals of motion are established that guarantee true boundary conditions for solitons, when they interact with the edge of the sample.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vortex light bullets in rotating Quasi-Phase-Matched photonic crystals","authors":"","doi":"10.1016/j.chaos.2024.115514","DOIUrl":"10.1016/j.chaos.2024.115514","url":null,"abstract":"<div><p>We present a methodology for the generation of stable vortex light bullets (LBs) in rotating Quasi-Phase-Matched (QPM) photonic crystals with quadratic nonlinearity. The photonic crystal is designed with a checkerboard structure, which is feasible to realize by using contemporary technological advancements. Within this framework, square- and rhombus-shaped LBs are observed, both of which are constructed as four-peak vortex mode. The control parameters include the effective phase mismatch, power, rotating frequency, and the size of checkerboard cells. These parameters play key roles in determining the distribution and stability domains of vortex LBs. In contrast to the stable vortex solitons observed in two-dimensional (2D) quadratic systems, the LBs investigated in the 3D rotating system exhibit narrower stability domains within the system’s parameter space. The rotating frequency results in the transition of LBs from quadrupole to traditional vortex modes. Potential applications of this research lie in the field of optical communications and information processing.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142232374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A method to regularize optimization problems governed by chaotic dynamical systems","authors":"","doi":"10.1016/j.chaos.2024.115491","DOIUrl":"10.1016/j.chaos.2024.115491","url":null,"abstract":"<div><p>Long-time averages of outputs from chaotic dynamical systems exhibit high-frequency oscillations in parameter space, which makes gradient-based optimization impractical. We show that these oscillations can be eliminated by coupling the initial and final states of the trajectory to produce discontinuous periodic orbits (DPOs). This approach can be regarded as a generalization of (continuous) unstable periodic orbits, which have been shown to regularize time-averages from chaotic problems. To solve the DPO governing equations, we present a Newton–Krylov algorithm that is globalized using a line search and parameter continuation. We study the accuracy of DPO-based outputs using the Lorenz dynamical system and the Kuramoto–Sivashinsky partial differential equation, and we demonstrate the effectiveness of DPO-based optimization on two simple examples. We conclude the paper with a discussion of open questions for future research.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142231789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Phase transitions in a heterogeneous lattice hydrodynamic model involving both communication distance and memory time duration differences","authors":"","doi":"10.1016/j.chaos.2024.115502","DOIUrl":"10.1016/j.chaos.2024.115502","url":null,"abstract":"<div><p>An in-depth analysis of vehicle heterogeneity characteristics in intelligent heterogeneous traffic flows, involving connected autonomous vehicles and human-driven vehicles, is essential to reveal the evolutionary mechanism of congestion and to understand its interaction among traffic factors. It has significant theoretical value in guiding the future field deployment and testing of large-scale connected autonomous vehicles through the systematic analysis of the complex dynamic characteristics of intelligent heterogeneous traffic flows from a traffic engineering perspective, as well as traffic management and control in intelligent heterogeneous traffic flow environments. In this study, the lattice hydrodynamics model is applied to construct a corresponding traffic flow model for the differences of communication capability and historical information memory capability for heterogeneous vehicles. The roles of these heterogeneous properties and their interactions are investigated. Through linear stability analysis and nonlinear analysis, we in this study explore the influence of key traffic factors involving the differences of communication capability and historical information memory capability contributing to ameliorating intelligent heterogeneous traffic dynamics, and numerical simulations are carried out to verify the accuracy and reliability of theoretical analysis. An interesting discovery is that longer memory duration gets better, but the optimizing impact of memory duration on the system being marginally decreasing.</p></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142229975","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}