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Int. J. Bifurc. Chaos最新文献

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Phases and Their Transitions Characterizing the Dynamics of Global Terrorism: A Multidimensional Scaling and Visualization Approach 表征全球恐怖主义动态的阶段及其转变:多维尺度和可视化方法
Pub Date : 2023-05-01 DOI: 10.1142/s0218127423500669
António M. Lopes
This paper proposes a technique based on unsupervised machine learning to find phases and phase transitions characterizing the dynamics of global terrorism. A dataset of worldwide terrorist incidents, covering the period from 1970 up to 2019 is analyzed. Multidimensional time-series concerning casualties and events are generated from a public domain database and are interpreted as the state of a complex system. The time-series are sliced, and the segments generated are objects that characterize the dynamical process. The objects are compared with each other by means of several distances and classified by means of the multidimensional scaling (MDS) method. The MDS generates loci of objects, where time is displayed as a parametric variable. The obtained portraits are analyzed in terms of the patterns of objects, characterizing the nature of the system dynamics. Complex dynamics are revealed, with periods resembling chaotic behavior, phases and phase transitions. The results demonstrate that the MDS is an effective tool to analyze global terrorism and can be adopted with other complex systems.
本文提出了一种基于无监督机器学习的技术来发现表征全球恐怖主义动态的阶段和相变。本文分析了1970年至2019年期间全球恐怖事件的数据集。有关伤亡和事件的多维时间序列是从公共领域数据库生成的,并被解释为复杂系统的状态。对时间序列进行切片,生成的片段是表征动态过程的对象。通过多个距离对目标进行比较,并采用多维尺度(MDS)方法对目标进行分类。MDS生成对象的轨迹,其中时间作为参数变量显示。根据对象的模式对获得的肖像进行分析,表征系统动力学的性质。揭示了复杂的动力学,具有类似混沌行为,相位和相变的周期。结果表明,MDS是分析全球恐怖主义的有效工具,可以应用于其他复杂系统。
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引用次数: 0
A Reaction-Diffusion-Advection Chemostat Model in a Flowing Habitat: Mathematical Analysis and Numerical Simulations 流动生境中的反应-扩散-平流变化学模型:数学分析与数值模拟
Pub Date : 2023-05-01 DOI: 10.1142/s0218127423500736
Wang Zhang, Hua Nie, Jianhua Wu
This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor.
本文研究了两种生物生长并竞争单一有限资源的反应-扩散-平流趋化模型。以两种植物的生长速率为可变参数,研究了生长速率对系统动力学的影响。研究发现,存在几个临界曲线,可以将该系统的动力学分为三种情景:(1)两个物种都灭绝;(二)竞争性排斥;(3)共存。此外,我们采用数值方法进一步了解上述临界曲线的潜在行为,并观察到除了竞争排斥和共存之外,还可能出现双稳态现象。为了进一步研究平流和扩散对系统动力学的影响,我们分别给出了随平流速率和扩散速率增加的单种模型和两种模型的正平衡解的分岔图。这些数值结果表明,平流和扩散在决定流动反应器中两种物质竞争的动力学中起着关键作用。
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引用次数: 1
Bifurcation of Limit Cycles by Perturbing Piecewise Linear Hamiltonian Systems with Piecewise Polynomials 用分段多项式扰动分段线性哈密顿系统极限环的分岔
Pub Date : 2023-04-01 DOI: 10.1142/s0218127423500591
Jiangbin Chen, Maoan Han
In this paper, we study a class of piecewise smooth near-Hamiltonian systems with piecewise polynomial perturbations. We first give the expression of the first order Melnikov function, and then estimate the number of limit cycles bifurcated from periodic annuluses by Melnikov function method. In addition, we discuss the number of limit cycles that can appear simultaneously near both sides of a generalized homoclinic or generalized double homoclinic loop.
本文研究了一类具有分段多项式摄动的分段光滑近哈密顿系统。首先给出了一阶Melnikov函数的表达式,然后用Melnikov函数法估计了由周期环分叉的极限环的个数。此外,我们还讨论了在广义同斜环或广义双同斜环两侧可以同时出现的极限环的数目。
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引用次数: 0
Stability of Periodic Orbits and Bifurcation Analysis of Ship Roll Oscillations in Regular Sea Waves 规则海浪中船舶横摇振荡周期轨道的稳定性及分岔分析
Pub Date : 2023-04-01 DOI: 10.1142/s021812742350058x
Ranjan Kumar, R. Mitra
Response, stability, and bifurcation of roll oscillations of a biased ship under regular sea waves are investigated. The primary and subharmonic response branches are traced in the frequency domain employing the Incremental Harmonic Balance (IHB) method with a pseudo-arc-length continuation approach. The stability of periodic responses and bifurcation points are determined by monitoring the eigenvalues of the Floquet transition matrix. The primary and higher-order subharmonic responses experience a cascade of period-doubling bifurcations, eventually culminating in chaotic responses detected by numerical integration (NI) of the equation of motion. Bifurcation diagrams are obtained through the period-doubling route to chaos. Solutions are aided with phase portrait, Poincaré map, time history and Fourier spectrum for better clarity as and when required. Finally, the same ship model is investigated under variable excitation moments that may result from different wave heights in regular seas. The biased ship roll model exhibits primary and subharmonic responses, jump phenomena, coexistence of multiple responses, and chaotically modulated motion. The stable, periodic, and steady-state roll responses obtained by the IHB method are validated by the NI method. Results obtained by both methods are found to agree very well.
研究了在规则海浪作用下偏置船舶横摇振动的响应、稳定性和分岔问题。采用伪弧长延拓的增量谐波平衡(IHB)方法在频域上跟踪了主谐波和次谐波响应分支。通过监测Floquet转移矩阵的特征值来确定周期响应和分岔点的稳定性。初级和高阶次谐波响应经历级联倍周期分岔,最终达到通过运动方程的数值积分(NI)检测到的混沌响应。通过混沌的倍周期路径得到了分岔图。解决方案辅助相肖像,庞加莱图,时间历史和傅立叶谱更好的清晰度,当需要的时候。最后,对同一船舶模型在正常海域不同浪高引起的不同激励矩下进行了研究。偏置船舶横摇模型表现出主次谐波响应、跳频现象、多重响应共存和混沌调制运动。用NI方法验证了IHB方法得到的稳定、周期和稳态侧滚响应。两种方法得到的结果非常吻合。
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引用次数: 0
Refined Composite Multiscale Phase Rényi Dispersion Entropy for Complexity Measure 复杂性度量的精细复合多尺度相r<s:1>色散熵
Pub Date : 2023-04-01 DOI: 10.1142/s0218127423500542
Yu-Han Tong, Guang Ling, Z. Guan, Qingju Fan, Li Wan
Assessing the complexity of signals or dynamical systems is important in disease diagnosis, mechanical system defect, astronomy analysis, and many other fields. Although entropy measures as complexity estimators have greatly improved, the majority of these measures are quite sensitive to specified parameters and are impacted by short data lengths. This paper proposes a novel entropy algorithm to enhance the existing complexity assessment methods based on classical dispersion entropy (DE) and Rényi entropy (RE) by introducing refined composite multiscale coarse-grained treatment and phase transformation. The proposed refined composite multiscale phase Rényi dispersion entropy (PRRCMDE) addresses the flaws of various existing entropy approaches while still incorporating their merits. Several simulated signals from logistic mapping, AR model, MIX process, and additive WGN periodic signals are adopted to examine the performance of PRRCMDE from multiple perspectives. It demonstrates that the efficacy of the suggested algorithm can be increased by modifying the DE and RE parameters to a reasonable range. As a real-world application, the bearings’ varied fault types and levels can also be recognized clearly.
评估信号或动力系统的复杂性在疾病诊断、机械系统缺陷、天文分析和许多其他领域都很重要。虽然熵测度作为复杂度估计器已经有了很大的改进,但是大多数熵测度对特定参数非常敏感,并且受到短数据长度的影响。针对现有的基于经典色散熵(DE)和rsamnyi熵(RE)的复杂性评估方法,本文提出了一种新的熵算法,通过引入精细复合多尺度粗粒度处理和相变,对现有的复杂性评估方法进行了改进。提出的改进复合多尺度相r尼米色散熵(PRRCMDE)方法在吸收现有熵方法优点的同时,解决了现有熵方法的缺陷。采用逻辑映射、AR模型、MIX过程和附加WGN周期信号等多个仿真信号,从多个角度考察了PRRCMDE的性能。结果表明,将DE和RE参数调整到合理的范围内,可以提高算法的有效性。作为实际应用,也可以清楚地识别轴承的各种故障类型和级别。
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引用次数: 0
Turing Bifurcation Induced by Cross-Diffusion and Amplitude Equation in Oncolytic Therapeutic Model: Viruses as Anti-Tumor Means 溶瘤治疗模型中交叉扩散诱导的图灵分岔和振幅方程:病毒作为抗肿瘤手段
Pub Date : 2023-04-01 DOI: 10.1142/s0218127423500621
F. Najm, R. Yafia, M. Aziz-Alaoui
In this paper, we propose a reaction–diffusion mathematical model augmented with self/cross-diffusion in 2D domain which describes the oncolytic virotherapy treatment of a tumor with its growth following the logistic law. The tumor cells are divided into uninfected and infected cells and the virus transmission is supposed to be in a direct mode (from cell to cell). In the absence of cross-diffusion, we establish well posedness of the problem, non-negativity and boundedness of solutions, nonexistence of positive solutions, local and global stability of the nontrivial steady-state and the nonoccurrence of Turing instability. In the presence of cross-diffusion, we prove the occurrence of Turing instability by using the cross-diffusion coefficient of infected cells as a parameter. To have an idea about different patterns, we derive the corresponding amplitude equation by using the nonlinear analysis theory. In the end, we perform some numerical simulations to illustrate the obtained theoretical results.
在本文中,我们提出了一个在二维域上增加自扩散/交叉扩散的反应扩散数学模型,该模型描述了肿瘤的生长遵循logistic规律的溶瘤病毒治疗。肿瘤细胞分为未感染细胞和感染细胞,病毒传播应该是直接模式(从细胞到细胞)。在没有交叉扩散的情况下,我们建立了问题的适定性、解的非负性和有界性、正解的不存在性、非平凡稳态的局部稳定性和全局稳定性以及图灵不稳定性的不发生性。在交叉扩散存在的情况下,我们用感染细胞的交叉扩散系数作为参数证明了图灵不稳定性的存在。为了了解不同的模式,我们利用非线性分析理论推导出相应的振幅方程。最后,对所得理论结果进行了数值模拟。
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引用次数: 0
Periodicity Analysis of the Logistic Map over Ring ℤ3n 环上Logistic映射的周期性分析
Pub Date : 2023-04-01 DOI: 10.1142/S0218127423500633
Xiaoxiong Lu, Eric Yong Xie, Chengqing Li
Periodicity analysis of sequences generated by a deterministic system is a long-standing challenge in both theoretical research and engineering applications. To overcome the inevitable degradation of the logistic map on a finite-precision circuit, its numerical domain is commonly converted from a real number field to a ring or a finite field. This paper studies the period of sequences generated by iterating the logistic map over ring [Formula: see text] from the perspective of its associated functional network, where every number in the ring is considered as a node, and the existing mapping relation between any two nodes is regarded as a directed edge. The complete explicit form of the period of the sequences starting from any initial value is given theoretically and verified experimentally. Moreover, conditions on the control parameter and initial value are derived, ensuring the corresponding sequences to achieve the maximum period over the ring. The results can be used as ground truth for dynamical analysis and cryptographical applications of the logistic map over various domains.
确定性系统产生的序列的周期性分析是理论研究和工程应用中一个长期存在的挑战。为了克服有限精度电路中逻辑映射不可避免的退化问题,通常将其数值域由实数域转换为环域或有限域。本文从环上逻辑映射的关联功能网络的角度研究环上逻辑映射迭代生成序列的周期[公式:见文],将环上的每一个数视为一个节点,将存在的任意两个节点之间的映射关系视为一条有向边。从理论上给出了从任意初值出发的序列周期的完备显式形式,并进行了实验验证。推导了控制参数和初始值的条件,保证了相应的序列在环上达到最大周期。该结果可作为逻辑映射在各种域上的动态分析和密码学应用的基础真理。
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引用次数: 8
Computing Invariant Densities of a Class of Piecewise Increasing Mappings 一类分段递增映射的不变密度计算
Pub Date : 2023-04-01 DOI: 10.1142/s0218127423500578
Zi Wang, Jiu Ding, N. Rhee
Let [Formula: see text] be a piecewise increasing mapping satisfying some generalized convexity condition, so that it possesses an invariant density that is a decreasing function. We show that this invariant density can be computed by a family of Markov finite approximations that preserve the monotonicity of integrable functions. We also construct a quadratic spline Markov method and demonstrate its merits numerically.
设[公式:见文]为满足某些广义凸性条件的分段递增映射,使其具有不变密度为递减函数。我们证明了这种不变密度可以用一组保持可积函数单调性的马尔可夫有限近似来计算。构造了二次样条马尔可夫方法,并用数值方法证明了其优点。
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引用次数: 0
Dynamics of a Coccinellids-Aphids Model with Stage Structure in Predator Including Maturation and Gestation Delays 含成熟期和妊娠期延迟的捕食者瓢虫-蚜虫阶段结构模型动力学
Pub Date : 2023-04-01 DOI: 10.1142/s0218127423500645
Mengran Yuan, Na Wang
This work studies a three-dimensional predator–prey model with gestation delay and stage structure between aphidophagous coccinellids and aphid pests, where the interaction between mature coccinellids and aphids is inscribed by Crowley–Martin functional response function, and immature coccinellids and aphids act in the form of Holling-I type. We prove the positivity and boundedness of the solution of the nondelayed system and analyze its equilibrium point, local asymptotic stability, and global stability. In addition to the delays, the critical values of Hopf bifurcation occurring for different parameters are also found from the numerical simulation. The stability of the delayed system and Hopf bifurcation with different delays as parameters are also discussed. Our model analysis shows that the time delay essentially governs the system’s dynamics, and the stability of the system switches as delays increase. We also investigate the direction and stability of the Hopf bifurcation using the normal form theory and center manifold theorem. Finally, we perform computer simulations and depict diagrams to support our theoretical results.
本文研究了食蚜瓢虫与蚜虫之间具有妊娠延迟和阶段结构的三维捕食-食饵模型,其中成熟瓢虫与蚜虫之间的相互作用由Crowley-Martin功能响应函数记录,未成熟瓢虫与蚜虫之间的相互作用以Holling-I型形式发生。证明了非延迟系统解的正性和有界性,并分析了其平衡点、局部渐近稳定性和全局稳定性。除了时滞外,数值模拟还得到了不同参数下Hopf分岔的临界值。讨论了时滞系统的稳定性和以不同时滞为参数的Hopf分岔问题。我们的模型分析表明,时间延迟本质上控制着系统的动力学,并且随着延迟的增加系统切换的稳定性。利用范式理论和中心流形定理研究了Hopf分岔的方向和稳定性。最后,我们进行了计算机模拟并绘制了图表来支持我们的理论结果。
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引用次数: 0
Dynamics of the Rotating Arm of an Electromechanical System Subjected to the Action of Circularly Placed Magnets: Numerical Study and Experiment 环形磁体作用下机电系统旋转臂的动力学:数值研究与实验
Pub Date : 2023-04-01 DOI: 10.1142/s0218127423500529
R. K. Tagne, P. Woafo, J. Awrejcewicz
This paper considers the experimental and numerical study of an electromechanical arm powered by a DC motor and subjected to the action of permanent magnets. The magnetic torques arise from permanent magnets mounted at the free end of the arm and along a circle. The electrical subsystem is powered by two forms of input signal (DC and AC voltage sources). For each case, we determine the condition for complete rotation of the mechanical arm versus the parameters of the system such as the arm length, the number of magnets, and the frequency of the external signal. The nonlinear dynamics of the system is examined by means of time-histories, bifurcation diagrams, Lyapunov exponents and phase portraits. Chaotic and periodic dynamics are detected numerically and confirmed experimentally.
本文对直流电机驱动永磁体作用下的机电臂进行了实验和数值研究。磁力矩来自安装在机械臂自由端沿圆周的永磁体。电气子系统由两种形式的输入信号(直流和交流电压源)供电。对于每种情况,我们确定机械臂完全旋转的条件与系统参数,如臂长,磁铁数量和外部信号的频率。系统的非线性动力学通过时程、分岔图、李亚普诺夫指数和相图来检验。对混沌动力学和周期动力学进行了数值检测和实验验证。
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引用次数: 0
期刊
Int. J. Bifurc. Chaos
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