International Journal of Bifurcation and Chaos最新文献_第3页

Stability and Bifurcation Analysis of a Spatially Size–Stage-Structured Model with Resting Phase 具有静止阶段的空间大小阶段结构模型的稳定性和分岔分析

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500603

Yajing Li, Zhihua Liu

引用次数: 0

Spatiotemporal and Trade-Off Dynamics in Prey–Predator Model with Domed Functional Response and Fear Effect 具有穹顶功能反应和恐惧效应的猎物-食肉动物模型中的时空动态和权衡动态

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500615

Masoom Bhargava, Anshu, Balram Dubey

{"title":"Spatiotemporal and Trade-Off Dynamics in Prey–Predator Model with Domed Functional Response and Fear Effect","authors":"Masoom Bhargava, Anshu, Balram Dubey","doi":"10.1142/s0218127424500615","DOIUrl":"https://doi.org/10.1142/s0218127424500615","url":null,"abstract":"In the ecological scenario, predators often risk their lives pursuing dangerous prey, potentially reducing their chances of survival due to injuries. Prey, on the other hand, try to strike a balance between reproduction rates and safety. In our study, we introduce a two-dimensional prey–predator model inspired by Tostowaryk’s work, specifically focusing on the domed-shaped functional response observed in interactions between pentatomid predators and neo-diprionid sawfly larvae. To account for the varying effectiveness of larval group defense, we incorporate a new component into the response equation. Our investigation delves into predator trade-off dynamics by adjusting the predator’s mortality rate to reflect losses incurred during encounters with dangerous prey and prey’s trade-off between safety and reproduction rate incorporating this domed-shaped functional response. Our model demonstrates bistability and undergoes various bifurcations, including transcritical, saddle-node, Hopf, Bogdanov–Takens, and Homoclinic bifurcations. Critical parameters impact both predator and prey populations, potentially leading to predator extinction if losses due to dangerous prey encounters become excessive, highlighting the risks predators face for their survival. Furthermore, the efficacy of group defense mechanisms can further endanger predators. Expanding our analysis to a spatially extended model under different perturbations, we explore Turing instability to explain the relationship between diffusion and encounter parameters through both stationary and dynamic pattern formation. Sensitivity to initial conditions uncovers spatiotemporal chaos. These findings provide valuable insights into comprehending the intricate dynamics of prey–predator interactions within ecological systems.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"85 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577480","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

Spatial Dynamics of a Competitive and Cooperative Model with Multiple Delay Effects: Turing Patterns and Hopf Bifurcation 具有多重延迟效应的竞争与合作模型的空间动力学：图灵模式与霍普夫分岔

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500627

Yu Mu, Wing-Cheong Lo

{"title":"Spatial Dynamics of a Competitive and Cooperative Model with Multiple Delay Effects: Turing Patterns and Hopf Bifurcation","authors":"Yu Mu, Wing-Cheong Lo","doi":"10.1142/s0218127424500627","DOIUrl":"https://doi.org/10.1142/s0218127424500627","url":null,"abstract":"Competing populations within an ecosystem often release chemicals during the interactions and diffusion processes. These chemicals can have diverse effects on competitors, ranging from inhibition to stimulation of species’ growth. This work constructs a competition model that incorporates stimulatory substances, spatial effects, and multiple time lags to investigate the combined impact of these phenomena on competitors’ growth. When the stimulation rate from the produced chemicals falls within a suitable threshold interval, all species within the system can coexist. Under the species’ coexistence, their diffusive phenomenon leads to a spatially heterogeneous distribution, resulting in patchy structures (Turing patterns) within their habitat. As the parameter values exceed their thresholds, species begin to exhibit spatially periodic oscillations (spatial Hopf bifurcation). The presence of multiple delays and competitors’ diffusion contributes to spatially complex and heterogeneous behaviors (Turing–Hopf bifurcation). The results help us understand the underlying mechanisms behind these heterogeneous behaviors and enable us to mitigate their negative impact on species’ growth and harvest. Numerical simulations are used to measure the dynamics of competitors under different parameter conditions.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"149 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577354","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

Exploring Iterated Implicit Function Systems: Existence and Properties of Attractors 探索迭代隐函数系统：吸引力的存在与特性

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500597

Zhong Dai, Shutang Liu

引用次数: 0

Computation of Normal Form and Unfolding of Codimension-3 Zero-Hopf–Hopf Bifurcation 标度-3 零-霍普夫-霍普夫分岔的正态计算与展开

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500639

Xin Xu, Xiaofang Zhang, Qinsheng Bi

{"title":"Computation of Normal Form and Unfolding of Codimension-3 Zero-Hopf–Hopf Bifurcation","authors":"Xin Xu, Xiaofang Zhang, Qinsheng Bi","doi":"10.1142/s0218127424500639","DOIUrl":"https://doi.org/10.1142/s0218127424500639","url":null,"abstract":"The computation of the normal form as well as its unfolding is a key step to understand the topological structure of a bifurcation. Though a lot of results have been obtained, it still remains unsolved for higher co-dimensional bifurcations. The main purpose of this paper is devoted to the computation of a codimension-3 zero-Hopf–Hopf bifurcation, at which a zero as well as two pairs of pure imaginary eigenvalues can be found from the matrix evaluated at the equilibrium point. Different distributions of eigenvalues are considered, which may behave in a non-semisimple form for 1:1 internal resonance. Based on the combination of center manifold and normal form theory, all the coefficients of normal forms and nonlinear transformations are derived explicitly in terms of parameters of the original vector field, which are obtained via a recursive procedure. Accordingly, a user friendly computer program using a symbolic computation language Maple is developed to compute the coefficients up to an arbitrary order for a specific vector field with zero-Hopf–Hopf bifurcation. Furthermore, universal unfolding parameters are derived in terms of the perturbation of physical parameters, which can be employed to investigate the local behaviors in the neighborhood of the bifurcation point. Here, we emphasize that though different norm forms based on different choices may exist, their topological structures are the same, corresponding to qualitatively equivalent dynamics.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"93 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577475","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

Emergence Behavior Versus Physical-Like Behavior 出现行为与类物理行为

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500548

Xiaobo Hou, Wanshan Lin, Xueting Tian, Xutong Zhao

引用次数: 0

Spatiotemporal Dynamics of a General Two-Species System with Taxis Term 带有的士项的一般双物种系统的时空动力学

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s021812742450055x

Wenjie Zuo, Yongli Song

{"title":"Spatiotemporal Dynamics of a General Two-Species System with Taxis Term","authors":"Wenjie Zuo, Yongli Song","doi":"10.1142/s021812742450055x","DOIUrl":"https://doi.org/10.1142/s021812742450055x","url":null,"abstract":"In this paper, we investigate the spatiotemporal dynamics in a diffusive two-species system with taxis term and general functional response, which means the directional movement of one species upward or downward the other one. The stability of positive equilibrium and the existences of Turing bifurcation, Turing–Hopf bifurcation and Turing–Turing bifurcation are investigated. An algorithm for calculating the normal form of the Turing–Hopf bifurcation induced by the taxis term and another parameter is derived. Furthermore, we apply our theoretical results to a cooperative Lotka–Volterra system and a predator–prey system with prey-taxis. For the cooperative system, stable equilibrium becomes unstable by taxis-driven Turing instability, which is impossible for the cooperative system without taxis. For a predator–prey system with prey-taxis, the dynamical classification near the Turing–Hopf bifurcation point is clearly described. Near the Turing–Hopf point, there are spatially inhomogeneous steady-state solution, spatially homogeneous/nonhomogeneous periodic solution and pattern transitions from one spatiotemporal state to another one.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"42 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577356","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

Periodic Orbit Dividing Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom – I 具有三个自由度的四元哈密顿系统中的周期轨道分割面 - I

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424300118

Francisco Gonzalez Montoya, Matthaios Katsanikas, Stephen Wiggins

{"title":"Periodic Orbit Dividing Surfaces in a Quartic Hamiltonian System with Three Degrees of Freedom – I","authors":"Francisco Gonzalez Montoya, Matthaios Katsanikas, Stephen Wiggins","doi":"10.1142/s0218127424300118","DOIUrl":"https://doi.org/10.1142/s0218127424300118","url":null,"abstract":"In prior work [Katsanikas & Wiggins, 2021a, 2021b, 2023c, 2023d], we introduced two methodologies for constructing Periodic Orbit Dividing Surfaces (PODS) tailored for Hamiltonian systems possessing three or more degrees of freedom. The initial approach, outlined in [Katsanikas & Wiggins, 2021a, 2023c], was applied to a quadratic Hamiltonian system in normal form having three degrees of freedom. Within this context, we provided a more intricate geometric characterization of this object within the family of 4D toratopes that describe the structure of the dividing surfaces discussed in these papers. Our analysis confirmed the nature of this construction as a dividing surface with the no-recrossing property. All these findings were derived from analytical results specific to the case of the Hamiltonian system discussed in these papers. In this paper, we extend our results for quartic Hamiltonian systems with three degrees of freedom. We prove for this class of Hamiltonian systems the no-recrossing property of the PODS and we investigate the structure of these surfaces. In addition, we compute and study the PODS in a coupled case of quartic Hamiltonian systems with three degrees of freedom.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"46 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577471","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

Crossing Limit Cycles in Planar Piecewise Linear Systems Separated by a Nonregular Line with Node–Node Type Critical Points 以节点-节点型临界点的非规则线分隔的平面片断线性系统中的交叉极限循环

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500494

Liping Sun, Zhengdong Du

{"title":"Crossing Limit Cycles in Planar Piecewise Linear Systems Separated by a Nonregular Line with Node–Node Type Critical Points","authors":"Liping Sun, Zhengdong Du","doi":"10.1142/s0218127424500494","DOIUrl":"https://doi.org/10.1142/s0218127424500494","url":null,"abstract":"In this paper, we investigate the existence and number of crossing limit cycles in a class of planar piecewise linear systems with node–node type critical points defined in two zones separated by a nonregular line formed by two rays emanated from the origin <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo stretchy=\"false\">)</mo></math>, which are the positive <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>x</mi></math>- and <math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>y</mi></math>-axes. We focus our attention on the existence of two-point crossing limit cycles, which intersect the switching line at two points. We obtain sufficient conditions under which the system has two two-point crossing limit cycles which intersect only one of the two rays. Moreover, we construct examples to show that this class of systems can have two, three or four two-point crossing limit cycles.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"61 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577855","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

Controlled Quasi-Latitudinal Solutions for Ultra-Fast Spin-Torque Magnetization Switching 超快自旋扭矩磁化切换的受控准纵向解决方案

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-04-09 DOI: 10.1142/s0218127424500561

Alessandro Fortunati, Massimiliano d’Aquino, Claudio Serpico

{"title":"Controlled Quasi-Latitudinal Solutions for Ultra-Fast Spin-Torque Magnetization Switching","authors":"Alessandro Fortunati, Massimiliano d’Aquino, Claudio Serpico","doi":"10.1142/s0218127424500561","DOIUrl":"https://doi.org/10.1142/s0218127424500561","url":null,"abstract":"The aim of this paper is to present a novel class of time-dependent controls to realize ultra-fast magnetization switching in nanomagnets driven by spin-torques produced by spin-polarized electric currents. Magnetization dynamics in such complex systems is governed by the Landau–Lifshitz–Slonczewski equation which describes the precessional motion of (dimensionless) magnetization vector on the unit-sphere. The relevant case of nanoparticles with uniaxial anisotropy having in-plane easy and intermediate axes as well as out-of-plane hard axis is considered. By exploiting the characteristic smallness of damping and spin-torque intensity, the complexity of the magnetic system’s dynamic is dealt with by employing tools borrowed from Hamiltonian Perturbation Theory. More precisely, the aforementioned controls are constructed via suitable perturbative tools in a way to realize approximate latitudinal solutions (i.e. motions on a sphere in which the out-of-plane magnetization component stays constant) with the effect to fast “switch” the system from one stationary state to another. The possibility to keep a (“small”) bounded value of the out-of-plane coordinate throughout this process of “transfer” turns out to be advantageous in the applications as it sensibly reduces the post-switching relaxation oscillations that may cause the failure of switching in real samples. Further relevant quantitative results on the behavior of the solutions during the pre- and post-switching stages (termed “expulsion” and “attraction”, respectively) are given as a by-product. A selection of validating numerical experiments is presented alongside the corresponding theoretical results.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"93 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577355","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