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International Journal of Bifurcation and Chaos最新文献

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Emergence of Hidden Strange Nonchaotic Attractors in a Rational Memristive Map 理性记忆图谱中隐藏的奇异非混沌吸引子的出现
IF 2.2 4区 数学
International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500172
Premraj Durairaj, Sathiyadevi Kanagaraj, Zhigang Zheng, Anitha Karthikeyan, Karthikeyan Rajagopal
{"title":"Emergence of Hidden Strange Nonchaotic Attractors in a Rational Memristive Map","authors":"Premraj Durairaj, Sathiyadevi Kanagaraj, Zhigang Zheng, Anitha Karthikeyan, Karthikeyan Rajagopal","doi":"10.1142/s0218127424500172","DOIUrl":"https://doi.org/10.1142/s0218127424500172","url":null,"abstract":"<p>To exemplify the existence of hidden strange nonchaotic attractors (HSNAs) and transition mechanism, we consider a rational memristive map with additional force. We find that the four-torus bifurcates into the eight-torus through torus doubling as a function of the control parameter. Following that, the formation of strange nonchaotic attractors occurs when increasing the control parameter. As a result, it is clear that the suggested rational maps reach hidden chaotic attractors via HSNAs through the route of torus doubling to torus breakdown. The obtained dynamical transitions are validated further using bifurcation analysis and the largest Lyapunov exponents. In particular, the obtained HSNAs are confirmed through distinct statistical measures including 0–1 test and singular continuous spectrum.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"40 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154136","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
From 1D Endomorphism to Multidimensional Hénon Map: Persistence of Bifurcation Structure 从一维内变形到多维赫农图谱：分叉结构的持续性
IF 2.2 4区 数学
International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500263
V. N. Belykh, N. V. Barabash, D. A. Grechko
{"title":"From 1D Endomorphism to Multidimensional Hénon Map: Persistence of Bifurcation Structure","authors":"V. N. Belykh, N. V. Barabash, D. A. Grechko","doi":"10.1142/s0218127424500263","DOIUrl":"https://doi.org/10.1142/s0218127424500263","url":null,"abstract":"<p>The renowned 2D invertible Hénon map turns into 1D noninvertible quadratic map when its leading parameter <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>b</mi></math></span><span></span> becomes zero. This well-known link was studied by Mira who demonstrated that the bifurcation set of Hénon diffeomorphism is similar to his “box-within-a-box” bifurcation structure of 1D endomorphism. In general, such similarity has not been strictly established, especially in multidimensional cases. In this paper, we proved that the Mira bifurcation structure of a quadratic noninvertible map persists when the parameter increases from zero and the map turns into an invertible multidimensional generalized Hénon map. The changes of periodic and homoclinic orbits and chaotic attractors at this transition are described. We proved the existence of Newhouse regions is different from those Mira boxes that accumulate to the homoclinic bifurcations.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"57 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154240","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
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
{"title":"3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – II","authors":"Matthaios Katsanikas, Stephen Wiggins","doi":"10.1142/s0218127424300052","DOIUrl":"https://doi.org/10.1142/s0218127424300052","url":null,"abstract":"<p>Our paper is a continuation of a previous work referenced as [Katsanikas &amp; Wiggins, 2024b]. In this new paper, we present a second method for computing three-dimensional generating surfaces in Hamiltonian systems with three degrees of freedom. These 3D generating surfaces are distinct from the Normally Hyperbolic Invariant Manifold (NHIM) and have the unique property of producing dividing surfaces with no-recrossing characteristics, as explained in our previous work [Katsanikas &amp; Wiggins, 2024b]. This second method for computing 3D generating surfaces is valuable, especially in cases where the first method is unable to achieve the desired results. This research aims to provide alternative techniques and solutions for addressing specific challenges in Hamiltonian systems with three degrees of freedom and improving the accuracy and reliability of generating surfaces. This research may find applications in the broader field of dynamical systems and attract the attention of researchers and scholars interested in these areas.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"25 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154363","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
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":"<p>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.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"44 1","pages":""},"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
{"title":"Dynamic Analysis of a Ratio-Dependent Food Chain Model with Prey-Taxis","authors":"Zhuzhen Liao, Cui Song, Zhi-Cheng Wang","doi":"10.1142/s0218127424500378","DOIUrl":"https://doi.org/10.1142/s0218127424500378","url":null,"abstract":"<p>In this paper, we consider a food chain model with ratio-dependent functional response and prey-taxis. We first investigate the global existence and boundedness of the unique positive classical solutions of the system in a bounded domain with smooth boundary and Neumann boundary conditions. Then, we analyze the local stability of the system and the existence of Hopf bifurcation. In addition, we prove the global asymptotic stability of steady states under some conditions by constructing a Lyapunov functional, and investigate convergence rates. Finally, we present several numerical simulations to illustrate the results.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"15 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124771","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
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":"<p>In this work, a dengue transmission model with logistic growth and time delay <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>τ</mi><mo stretchy=\"false\">)</mo></math></span><span></span> 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 <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>τ</mi><mo>=</mo><mn>0</mn></math></span><span></span>, 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.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"74 1","pages":""},"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":"<p>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 <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>. In this paper, our main goal is to examine a class of discontinuous piecewise differential systems in <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>, 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.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"23 1","pages":""},"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
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
{"title":"Dynamics of a Class of Prey–Predator Models with Singular Perturbation and Distributed Delay","authors":"Jie Gao, Yue Zhang","doi":"10.1142/s0218127424500317","DOIUrl":"https://doi.org/10.1142/s0218127424500317","url":null,"abstract":"<p>In this paper, two prey–predator models with distributed delays are presented based on the growth and loss rates of the predator, which are much smaller than that of the prey, leading to a singular perturbation problem. It is obtained that Hopf bifurcation can occur, where the coexistence equilibrium becomes unstable leading to a stable limit cycle. Subsequently, considering the perturbation parameter <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mn>0</mn><mo>&lt;</mo><mi>𝜀</mi><mo>≪</mo><mn>1</mn></math></span><span></span>, the fact that the solution crossing the transcritical point converges to a stable equilibrium is discussed for the model with Holling type I using the linear chain criterion, center-manifold reduction, the geometric singular perturbation theory and entry–exit function. The existence and uniqueness of relaxation oscillation cycle for the model with Holling type II are obtained. In addition, numerical simulations are provided to verify the analytical results.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"26 3 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124677","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
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
{"title":"A Lightweight CNN Based on Memristive Stochastic Computing for Electronic Nose","authors":"Bin Yang, Tao Chen, Ai Chen, Shukai Duan, Lidan Wang","doi":"10.1142/s0218127424500275","DOIUrl":"https://doi.org/10.1142/s0218127424500275","url":null,"abstract":"<p>Gas detection plays different roles in different environments. Traditional algorithms implemented on electronic nose for gas detection and recognition have high complexity and cannot resist device drift. In response to the above issues, we propose a convolutional neural network based on memristive Stochastic Computing (SC), which combines the characteristics of small devices and low power consumption of memristor devices, as well as the fast and fault-tolerant random calculation speed. It can effectively utilize hardware advantages, recognizing gases by electronic nose. The experimental results show that for two different gas sensor array datasets, the accuracy of the proposed method can achieve the level of 99%. When using memristive SC for deduction, the accuracy decreases by less than 1%, but in drift data, the accuracy can be improved by about 3%. Finally, the improvement in area, power, and energy compared to inference in GPU (NVIDIA Geforce RTX 3060 Laptop) is 1104X, 48X, and 9X, respectively.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"33 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129802","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 and Exact Solutions of a Cantilever Beam Vibration Model Without Damping and Forced Terms 无阻尼和强制项悬臂梁振动模型的分岔和精确解
IF 2.2 4区 数学
International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500391
Jinsen Zhuang, Guanrong Chen, Jibin Li
{"title":"Bifurcations and Exact Solutions of a Cantilever Beam Vibration Model Without Damping and Forced Terms","authors":"Jinsen Zhuang, Guanrong Chen, Jibin Li","doi":"10.1142/s0218127424500391","DOIUrl":"https://doi.org/10.1142/s0218127424500391","url":null,"abstract":"<p>For the cantilever beam vibration model without damping and forced terms, the corresponding differential system is a planar dynamical system with some singular straight lines. In this paper, by using the techniques from dynamical systems and singular traveling wave theory developed by [Li &amp; Chen, 2007] to analyze its corresponding differential system, the bifurcations and the dynamical behaviors of the corresponding phase portraits are identified and analyzed. Under different parameter conditions, exact homoclinic and heteroclinic solutions, periodic solutions, compacton solutions, as well as peakons and periodic peakons, are all found explicitly.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"15 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124778","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
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