International Journal of Bifurcation and Chaos最新文献_第10页

Ultra-Chaos in the Motion of Walking Droplet 行走水滴运动中的超混沌现象

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501912

Yu Yang, Shijie Qin, Shijun Liao

{"title":"Ultra-Chaos in the Motion of Walking Droplet","authors":"Yu Yang, Shijie Qin, Shijun Liao","doi":"10.1142/s0218127423501912","DOIUrl":"https://doi.org/10.1142/s0218127423501912","url":null,"abstract":"A liquid bath vibrating vertically can lead to the emergence of a self-propelled walking droplet on its free surface, which can exhibit chaotic motion. It is well-known that trajectories of a chaotic system are sensitive to its initial condition, known as the “butterfly-effect”, while its statistics normally remain stable to small disturbances: this type of chaos is called “normal-chaos”. However, a concept called “ultra-chaos” has been recently introduced, whose statistical features are unstable, i.e. extremely sensitive to small disturbances. Up to now, a few examples of ultra-chaos have been reported. In this paper, the influence of tiny disturbances on the motion of walking droplet is investigated. It is found that both normal-chaos and ultra-chaos exist in the motion of the walking droplet. Different from the normal-chaotic motion, even the statistical properties of the droplet’s ultra-chaotic motion are sensitive to tiny disturbances. Therefore, this illustrates once again that ultra-chaos indeed exists widely and represents a higher disorder compared with normal-chaos. The ultra-chaos as a new concept can widen our knowledge about chaos and provide us with a new point of view to study chaotic properties. It should be emphasized that, for an ultra-chaos, it is impossible to repeat any results of its physical experiments or numerical simulations even in the meaning of statistics! Unfortunately, reproducibility is a corner stone of modern science. Thus, the paradigm of modern scientific research might be invalid for an ultra-chaotic system.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139140397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Experimental Observation of Extreme Events in the Shimizu Morioka Oscillator 清水盛冈振荡器极端事件的实验观测

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423300392

K. Thamilmaran, T. Thamilvizhi, S. Kumarasamy, Premraj Durairaj

{"title":"Experimental Observation of Extreme Events in the Shimizu Morioka Oscillator","authors":"K. Thamilmaran, T. Thamilvizhi, S. Kumarasamy, Premraj Durairaj","doi":"10.1142/s0218127423300392","DOIUrl":"https://doi.org/10.1142/s0218127423300392","url":null,"abstract":"In this study, we investigate the occurrence of dragon-king extreme events in a three-dimensional autonomous Shimizu–Morioka oscillator. We observe that the bounded chaotic oscillations transition into large amplitude extreme events at a critical value of the system control parameter triggered by an interior crisis. These extreme events exhibit a unique distribution characterized by the probability distribution function. We performed laboratory experiments and conducted rigorous numerical simulations on the Shimizu–Morioka oscillator to validate our findings. The results from both approaches are in excellent agreement and confirm extreme behavior in this autonomous system. Our study represents the first comprehensive investigation of extreme events in the Shimizu–Morioka oscillator, integrating experimental observations and numerical simulations. Also, we observed the dragon-king extreme events in both experimental and numerical studies. These findings enhance our understanding of extreme events and their potential applications in chaos-based dynamical systems, contributing to advancing this field.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139141438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Dynamic Analysis of a Dual-Channel Closed-Loop Supply Chain with Heterogeneous Players and a Delay Decision 具有异构参与者和延迟决策的双通道闭环供应链的动态分析

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501870

Yu-Han Zhang, Tao Zhang

{"title":"Dynamic Analysis of a Dual-Channel Closed-Loop Supply Chain with Heterogeneous Players and a Delay Decision","authors":"Yu-Han Zhang, Tao Zhang","doi":"10.1142/s0218127423501870","DOIUrl":"https://doi.org/10.1142/s0218127423501870","url":null,"abstract":"This paper considers a dual-channel closed-loop supply chain (CLSC) consisting of a manufacturer who wholesales new products through the traditional retail channel and distributes remanufactured products via a direct (online) channel established by himself. Two dynamical Stackelberg game models are developed based on the assumption that the retailer is an adaptive player, and the manufacturer is a bounded rational player who may adopt a delay decision. The existence and locally asymptotic stability of the Nash equilibrium are examined. Moreover, the impacts of key parameters on the complexity characteristics of the models and the performance of chain members are studied by numerical simulation. The results reveal that the excessively fast price adjustment speeds of the manufacturer, the larger consumers’ discount perception for the remanufactured products, and the consumers’ preference for the direct channel have a strong destabilizing effect on the Nash equilibrium’s stability. Furthermore, the delay decision implemented by the manufacturer could be a stabilizing or destabilizing factor for the system. The manufacturer will tolerate a considerable profit reduction while the retailer gains more profits when the dual-channel CLSC system enters periodic cycles and chaotic motions.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139141711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Symmetry, Multistability and Antimonotonicity of a Shinriki Oscillator with Dual Memristors 带双 Memristors 的神力振荡器的对称性、多稳定性和反谐调性

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501869

Yizi Cheng, Fuhong Min

{"title":"Symmetry, Multistability and Antimonotonicity of a Shinriki Oscillator with Dual Memristors","authors":"Yizi Cheng, Fuhong Min","doi":"10.1142/s0218127423501869","DOIUrl":"https://doi.org/10.1142/s0218127423501869","url":null,"abstract":"In this paper, a type of modified dual memristive Shinriki oscillator is constructed with a flux-controlled absolute-type memristor and a voltage-controlled generic memristor, and the proposed oscillator with abundant dynamical behaviors, including the multistability and antimonotonicity, is comprehensively studied through dynamical distribution graphs, bifurcation diagrams, Lyapunov exponents and phase portraits. It is found that the passive/active state of memristor, which means different characteristics in the [Formula: see text]–[Formula: see text] domain with positive and negative parameters of the elements, can affect the state of the oscillator. For example, if the memristor is active, the oscillator will change more frequently in the multistable region. Also, it is noted that, for inherent initial-related symmetry and circuit structures with duality, both phenomena have strong symmetric characteristics and opposite evolution trends modulated by values of corresponding components. Especially, the bubbles, which are symmetric about parameters with duality and own complex evolution laws, have rarely been explored in previous works. In addition, the memristive oscillator is modularized based on field programmable gate array (FPGA) technology, and the multiple coexisting attractors are captured, which verifies the accuracy of the numerical results.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139140992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Structurally Unstable Synchronization and Border-Collision Bifurcations in the Two-Coupled Izhikevich Neuron Model 双耦合伊齐克维奇神经元模型中结构不稳定的同步和边界碰撞分岔

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423300409

Y. Miino, T. Ueta

{"title":"Structurally Unstable Synchronization and Border-Collision Bifurcations in the Two-Coupled Izhikevich Neuron Model","authors":"Y. Miino, T. Ueta","doi":"10.1142/s0218127423300409","DOIUrl":"https://doi.org/10.1142/s0218127423300409","url":null,"abstract":"This study investigates a structurally unstable synchronization phenomenon observed in the two-coupled Izhikevich neuron model. As the result of varying the system parameter in the region of parameter space close to where the unstable synchronization is observed, we find significant changes in the stability of its periodic motion. We derive a discrete-time dynamical system that is equivalent to the original model and reveal that the unstable synchronization in the continuous-time dynamical system is equivalent to border-collision bifurcations in the corresponding discrete-time system. Furthermore, we propose an objective function that can be used to obtain the parameter set at which the border-collision bifurcation occurs. The proposed objective function is numerically differentiable and can be solved using Newton’s method. We numerically generate a bifurcation diagram in the parameter plane, including the border-collision bifurcation sets. In the diagram, the border-collision bifurcation sets show a novel bifurcation structure that resembles the “strike-slip fault” observed in geology. This structure implies that, before and after the border-collision bifurcation occurs, the stability of the periodic point discontinuously changes in some cases but maintains in other cases. In addition, we demonstrate that a border-collision bifurcation set successively branches at distinct points. This behavior results in a tree-like structure being observed in the border-collision bifurcation diagram; we refer to this structure as a border-collision bifurcation tree. We observe that a periodic point disappears at the border-collision bifurcation in the discrete-time dynamical system and is simultaneously replaced by another periodic point; this phenomenon corresponds to a change in the firing order in the continuous-time dynamical system.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139141837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Dynamics of a Reaction–Diffusion–Advection System with Nonlinear Boundary Conditions 具有非线性边界条件的反应-扩散-平流系统的动力学特性

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501936

Chenyuan Tian, Shangjiang Guo

引用次数: 0

Relaxation Oscillations in an SIS Epidemic Model with a Nonsmooth Incidence 具有非光滑发病率的 SIS 流行病模型中的松弛振荡

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501882

Yingying Zhang, Ruijuan Niu

引用次数: 0

Existence and Number of Figure-Eight Loops in Planar Sector-Wise Linear Systems with Saddle–Saddle Dynamics 具有马鞍-马鞍动力学的平面扇形线性系统中图-八环路的存在与数量

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501985

Xiao-Juan Liu, Song-Mei Huan

引用次数: 0

Bifurcations in a General Delay Sel’kov–Schnakenberg Reaction–Diffusion System 一般延迟塞尔科夫-施纳肯伯格反应-扩散系统中的分岔

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s021812742350195x

Yanqiu Li, Lei Zhang

引用次数: 0

Dynamical Analysis of a Predator–Prey Model with Additive Allee Effect and Migration 带有加性阿利效应和迁移的捕食者-猎物模型的动态分析

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-11 DOI: 10.1142/s0218127423501791

Xinhao Huang, Lijuan Chen, Yue Xia, Fengde Chen

引用次数: 0