International Journal of Bifurcation and Chaos最新文献_第6页

Infinitely Many Coexisting Attractors and Scrolls in a Fractional-Order Discrete Neuron Map 分数阶离散神经元图谱中的无限多共存吸引子和卷轴

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501973

Lujie Ren, Lei Qin, Hadi Jahanshahi, Jun Mou

引用次数: 0

The Extended 16th Hilbert Problem for Discontinuous Piecewise Systems Formed by Linear Centers and Linear Hamiltonian Saddles Separated by a Nonregular Line 由线性中心和线性哈密顿鞍构成的、被非规则线分隔的不连续片断系统的扩展第 16 希尔伯特问题

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501961

Jaume Llibre, C. Valls

引用次数: 0

Chaotic Model of Muscle and Joint Interactions Based on CPG for Rehabilitation of Incomplete Spinal Cord Injury Patients 基于 CPG 的肌肉与关节相互作用混沌模型用于不完全脊髓损伤患者的康复治疗

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501894

Monireh Maleki, F. N. Rahatabad, Majid Pouladian

{"title":"Chaotic Model of Muscle and Joint Interactions Based on CPG for Rehabilitation of Incomplete Spinal Cord Injury Patients","authors":"Monireh Maleki, F. N. Rahatabad, Majid Pouladian","doi":"10.1142/s0218127423501894","DOIUrl":"https://doi.org/10.1142/s0218127423501894","url":null,"abstract":"The aim of modeling musculoskeletal systems is to understand the mechanisms of locomotion control in terms of neurophysiology and neuroanatomy. The complexity and unique nature of neuromuscular systems, however, make control problems in these systems very challenging due to several characteristics including speed and precision. Thus, their investigation requires the use of simple and analyzable methods. Consequently, taking into account the central pattern generator’s (CPG) function, we attempted to create a structured chaotic model of how human joints and muscles interact for the purpose of facilitating gait and rehabilitation in patients with incomplete spinal cord injury. The four muscle groups used in this model are gluteus, and hip flexor groups for flexion and extension of the hip joints as well as hamstring muscles and vasti muscles for flexion and extension of the knee joint. The results indicate that the output of the chaotic model of muscle and joint interactions in a healthy state would be chaotic, while in the incomplete spinal cord injury state, it would remain a fixed point. For model rehabilitation, afferent nerve stimulation is used in a CPG model; based on the modeling results, by applying coefficients of 1.98, 2.21, and 3.1 to the values of Ia, II, and Ib afferent nerves, the incomplete spinal cord injury model state is changed from a fix-point to periodic in a permanent fashion, suggesting locomotion with rehabilitation in our model. Based on the results obtained from the chaotic model of muscle and joint interactions as well as the comparisons made with reference papers, it can be stated that this model has acceptable output while enjoying simple computations and can predict different norms.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 13","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139137739","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

Complex Dynamics and Fractional-Order Optimal Control of an Epidemic Model with Saturated Treatment and Incidence 具有饱和治疗和发病率的流行病模型的复杂动力学和分数阶最优控制

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501924

Suvankar Majee, T. K. Kar, Soovoojeet Jana, D. K. Das, J. J. Nieto

{"title":"Complex Dynamics and Fractional-Order Optimal Control of an Epidemic Model with Saturated Treatment and Incidence","authors":"Suvankar Majee, T. K. Kar, Soovoojeet Jana, D. K. Das, J. J. Nieto","doi":"10.1142/s0218127423501924","DOIUrl":"https://doi.org/10.1142/s0218127423501924","url":null,"abstract":"In this study, we have developed a novel SIR epidemic model by incorporating fractional-order differential equations and utilizing saturated-type functions to describe both disease incidence and treatment. The intricate dynamical characteristics of the proposed model, encompassing the determination of the conditions for the existence of all possible feasible equilibria with their local and global stability criteria, are investigated thoroughly. The model undergoes backward bifurcation with respect to the parameter representing the side effects due to treatment. This phenomenon emphasizes the critical role of treatment control parameters in shaping epidemic outcomes. In addition, to understand the optimal role of the treatment in mitigating the disease prevalence and minimizing the associated cost, we investigated a fractional-order optimal control problem. To further visualize the analytical results, we have conducted simulation works considering feasible parameter values for the model. Finally, we have employed local and global sensitivity analysis techniques to identify the factors that have the greatest potential to reduce the impact of the disease.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 17","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139138198","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

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":" 3","pages":""},"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":" 44","pages":""},"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":" 38","pages":""},"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":" 6","pages":""},"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":" 29","pages":""},"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

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