International Journal of Bifurcation and Chaos最新文献_第8页

3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – II 具有三个自由度的哈密顿系统中的 3D 生成曲面 - II

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424300052

Matthaios Katsanikas, Stephen Wiggins

引用次数: 0

Transition and Propagation of Epilepsy in an Improved Epileptor Model Coupled with Astrocyte 与星形胶质细胞耦合的改进型癫痫模型中的癫痫过渡与传播

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-11 DOI: 10.1142/s0218127424300076

Kangning An, Lin Du, Honghui Zhang, Zhuan Shen, Xiaojuan Sun

{"title":"Transition and Propagation of Epilepsy in an Improved Epileptor Model Coupled with Astrocyte","authors":"Kangning An, Lin Du, Honghui Zhang, Zhuan Shen, Xiaojuan Sun","doi":"10.1142/s0218127424300076","DOIUrl":"https://doi.org/10.1142/s0218127424300076","url":null,"abstract":"In this paper, a tripartite synapse network is constructed to examine external and internal triggering factors of epilepsy transition and propagation in neurons with the Epileptor-2 model. We first explore the external stimuli in the environment that induce epileptic activities and transition behaviors among Ictal Discharges (IDs) and Interictal Discharges (IIDs) states. The higher the strength and abruptness of the stimuli, the more severe is the occurrence of epilepsy within a reasonable range of parameters. Then for the internal triggering factors, the results of the tripartite synapse network, which is improved by combining the Epileptor-2 model with astrocyte by means of ion exchange and new connections, show that astrocytes can transmit normal physiological activity information and filter out abnormal discharge information of neurons. One of the causes for epileptic seizures is the abnormal release of glial neurotransmitters in astrocytes. The excessive release of glutamate causes the discharge state of neurons to transit from nonepileptic to IIDs, IDs and tonic, while adenosine triphosphate can alleviate epilepsy. Meanwhile, the synapse dysfunction of an astrocyte-free network can also lead to seizures, and the epilepsy propagation ability of a tripartite synapse network becomes weaker than that of an astrocyte-free network. Our research is expected to provide some theoretical basis for the therapeutic approach to curing epilepsy in the intracellular and extracellular contexts.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124776","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 Ratio-Dependent Food Chain Model with Prey-Taxis 带有猎物-税收的比例依赖型食物链模型的动态分析

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-09 DOI: 10.1142/s0218127424500378

Zhuzhen Liao, Cui Song, Zhi-Cheng Wang

引用次数: 0

Stability Analysis and Simulation of a Delayed Dengue Transmission Model with Logistic Growth and Nonlinear Incidence Rate 具有逻辑增长和非线性发病率的延迟登革热传播模型的稳定性分析与模拟

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500287

Fangkai Guo, Xiaohong Tian

{"title":"Stability Analysis and Simulation of a Delayed Dengue Transmission Model with Logistic Growth and Nonlinear Incidence Rate","authors":"Fangkai Guo, Xiaohong Tian","doi":"10.1142/s0218127424500287","DOIUrl":"https://doi.org/10.1142/s0218127424500287","url":null,"abstract":"In this work, a dengue transmission model with logistic growth and time delay <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>τ</mi><mo stretchy=\"false\">)</mo></math> is investigated. Through detailed mathematical analysis, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed, the existence of Hopf bifurcation and stability switch is established, and it is proved that the system is permanent if the basic reproduction number is greater than 1. On the basis of Lyapunov functional and LaSalle’s invariance principle, sufficient conditions are derived for the global stability of the endemic equilibrium. The primary theoretical results are simulated numerically. In addition, when <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>τ</mi><mo>=</mo><mn>0</mn></math>, relevant properties of the Hopf bifurcation are analyzed. Finally, sensitivity analysis is given and data fitting is carried out to predict the epidemic development trend of dengue fever in Singapore in 2020.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124769","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

Four Limit Cycles of Three-Dimensional Discontinuous Piecewise Differential Systems Having a Sphere as Switching Manifold 以球面为切换平面的三维非连续片断微分系统的四个极限循环

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500305

Louiza Baymout, Rebiha Benterki

{"title":"Four Limit Cycles of Three-Dimensional Discontinuous Piecewise Differential Systems Having a Sphere as Switching Manifold","authors":"Louiza Baymout, Rebiha Benterki","doi":"10.1142/s0218127424500305","DOIUrl":"https://doi.org/10.1142/s0218127424500305","url":null,"abstract":"Because of their applications, the study of piecewise-linear differential systems has become increasingly important in recent years. This type of system already exists to model many different natural phenomena in physics, biology, economics, etc. As is well known, the study of the qualitative theory of piecewise differential systems focuses mainly on limit cycles. Most papers studying the problem of existence and the maximum number of limit cycles of piecewise differential systems have precisely considered planar systems. However, few papers have examined this problem in <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mn>3</mn></mrow></msup></math>. In this paper, our main goal is to examine a class of discontinuous piecewise differential systems in <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mn>3</mn></mrow></msup></math>, where we consider the unit sphere as the separation surface that divides the entire space into two regions, each one has a linear vector field analogous to planar center. In general, it is hard to determine an exact upper bound for the number of limit cycles that a class of differential systems can exhibit. We prove that this class of differential systems can have at most four limit cycles. We show that there are examples of such differential systems with exactly 1, 2, 3 and 4 limit cycles.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124792","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

Existence and Uniqueness of a Canard Cycle with Cyclicity at Most Two in a Singularly Perturbed Leslie–Gower Predator–Prey Model with Prey Harvesting 具有猎物捕获功能的奇异扰动莱斯利-高尔捕食者-猎物模型中周期性最多为 2 的卡纳周期的存在性和唯一性

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500366

Zhenshu Wen, Tianyu Shi

引用次数: 0

Geometrical and Numerical Analysis of Predator–Prey System Based on the Allee Effect in Predator 基于捕食者阿利效应的捕食者-猎物系统几何与数值分析

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500330

M. K. Gupta, Abha Sahu, C. K. Yadav

{"title":"Geometrical and Numerical Analysis of Predator–Prey System Based on the Allee Effect in Predator","authors":"M. K. Gupta, Abha Sahu, C. K. Yadav","doi":"10.1142/s0218127424500330","DOIUrl":"https://doi.org/10.1142/s0218127424500330","url":null,"abstract":"This study explores the complex dynamics of the predator–prey interactions, with a specific emphasis on the influence of the Allee effect on the predator population. We examined the fundamental mathematical characteristics of the model under consideration, such as the positivity of the system and the boundedness of the solutions. We investigated the equilibrium points and analyzed their stability using the Jacobi and Lyapunov methods. A comprehensive examination was carried out on the geometric properties of the dynamical system to compute the five invariants of the KCC theory. In particular, the deviation curvature tensor and its eigenvalues are investigated to demonstrate the behavior of the system stability. We have also obtained the necessary and sufficient conditions for the given set of parameters of the system in order to have the Jacobi stability (instability) near the equilibrium point. To visualize the dynamical behavior of the predator–prey model with the Allee effect in the predator density, numerical simulations were conducted. The investigation encompasses an examination of the system’s behavior from both geometric and numerical standpoints, with the objective of attaining a thorough comprehension using few examples.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140078899","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 Class of Prey–Predator Models with Singular Perturbation and Distributed Delay 具有奇异扰动和分布式延迟的一类猎物-食肉动物模型的动力学特性

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500317

Jie Gao, Yue Zhang

引用次数: 0

A Lightweight CNN Based on Memristive Stochastic Computing for Electronic Nose 基于 Memristive 随机计算的轻量级电子鼻 CNN

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500275

Bin Yang, Tao Chen, Ai Chen, Shukai Duan, Lidan Wang

引用次数: 0

Global Phase Portraits of Piecewise Quadratic Differential Systems with a Pseudo-Center 带伪中心的片断二次微分系统的全局相位肖像

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500329

Meriem Barkat, R. Benterki, Enrique Ponce

引用次数: 0