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

Slow Invariant Manifolds of Memristor-Based Chaotic Circuits 基于 Memristor 的混沌电路的慢速不变频域

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424300039

Jean-Marc Ginoux, Riccardo Meucci, Guanrong Chen, Leon O. Chua

引用次数: 0

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

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424300040

Matthaios Katsanikas, Stephen Wiggins

{"title":"3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – I","authors":"Matthaios Katsanikas, Stephen Wiggins","doi":"10.1142/s0218127424300040","DOIUrl":"https://doi.org/10.1142/s0218127424300040","url":null,"abstract":"In our earlier research (see [Katsanikas & Wiggins, 2021a, 2021b, 2023a, 2023b, 2023c]), we developed two methods for creating dividing surfaces, either based on periodic orbits or two-dimensional generating surfaces. These methods were specifically designed for Hamiltonian systems with three or more degrees of freedom. Our prior work extended these dividing surfaces to more complex structures such as tori or cylinders, all within the energy surface of the Hamiltonian system. In this paper, we introduce a new method for constructing dividing surfaces. This method differs from our previous work in that it is based on 3D surfaces or geometrical objects, rather than periodic orbits or 2D generating surfaces (see [Katsanikas & Wiggins, 2023a]). To explain and showcase the new method and to present the structure of these 3D surfaces, the paper provides examples involving Hamiltonian systems with three degrees of freedom. These examples cover both uncoupled and coupled cases of a quadratic normal form Hamiltonian system. Our current paper is the first in a series of two papers on this subject. This research is likely to be of interest to scholars and researchers in the field of Hamiltonian systems and dynamical systems, as it introduces innovative approaches to constructing dividing surfaces and exploring their applications.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"23 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154042","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 Complexities in Competing Parasitoid Species on a Shared Host 寄生虫物种在共同寄主上竞争的动态复杂性

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500147

Lijiao Jia, Yunil Roh, Guangri Piao, Il Hyo Jung

引用次数: 0

Optimal and Poor Synchronizations of Directionally Coupled Phase-Coherent Chaotic Oscillators 定向耦合相位相干混沌振荡器的最佳同步和不良同步

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500238

Yong Lei, Xin-Jian Xu, Xiaofan Wang

{"title":"Optimal and Poor Synchronizations of Directionally Coupled Phase-Coherent Chaotic Oscillators","authors":"Yong Lei, Xin-Jian Xu, Xiaofan Wang","doi":"10.1142/s0218127424500238","DOIUrl":"https://doi.org/10.1142/s0218127424500238","url":null,"abstract":"We study directionally coupled phase-coherent chaotic oscillators in complex networks. We introduce an adjusted Lyapunov function that incorporates the frequencies of the oscillators and the interaction structure. Using the well-known Rössler system as an example, we address two optimization problems: frequency allocation and network design. Through numerical experiments, we demonstrate that the systematic synchrony can be effectively enhanced or inhibited by minimizing or maximizing the objective function, respectively. We then delve into the relationship between the structural and dynamical properties that lead to optimal synchronization. Interestingly, we observe a positive correlation between nodal in-degrees and frequency magnitudes, indicating that nodes with higher in-degrees tend to exhibit larger frequency magnitudes. On the other hand, we also find a negative correlation between nodal frequency and adjacent in-frequencies, suggesting that nodes with higher frequencies tend to be surrounded by nodes with lower frequency values. Finally, we explore the connections between degree correlations and optimal synchronization. We find that when minimizing the objective function, the presence of degree correlations always inhibits the systematic synchrony for frequency allocation, while the act of network design causes the correlations to become negative.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"85 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154035","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

Study of Short-Term and Long-Term Memories by Hodgkin–Huxley Memristor 利用霍奇金-赫胥黎记忆器研究短期和长期记忆

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500408

L. Wen, C. K. Ong

{"title":"Study of Short-Term and Long-Term Memories by Hodgkin–Huxley Memristor","authors":"L. Wen, C. K. Ong","doi":"10.1142/s0218127424500408","DOIUrl":"https://doi.org/10.1142/s0218127424500408","url":null,"abstract":"Long-term memory (LTM ) and short-term memory (STM ) and their evolution from one to the other are important mechanisms to understand brain memory. We use the Hodgkin–Huxley (HH ) model, a well-tested and closest model to biological neurons and synapses, to shine some light on LTM and STM memorization mechanisms. The role of <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">Na</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math> and <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">K</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math>ion channels playing in LTM and STM process is carefully examined by using three different types of input signals, namely, a step DC voltage, a positive part of sinusoidal wave and periodic square signal with read voltage. Results are analyzed based on first-order<math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">K</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math>memristor and second-order<math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mstyle><mtext mathvariant=\"normal\">Na</mtext></mstyle></mrow><mrow><mo stretchy=\"false\">+</mo></mrow></msup></math>memristor.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"16 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154119","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, Bifurcation and Dynamics in a Network with Delays 有延迟网络的稳定性、分岔和动态性

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500251

Xu Xu, Jianming Liu

{"title":"Stability, Bifurcation and Dynamics in a Network with Delays","authors":"Xu Xu, Jianming Liu","doi":"10.1142/s0218127424500251","DOIUrl":"https://doi.org/10.1142/s0218127424500251","url":null,"abstract":"In real-world networks, due to complex topological structures and uncertainties such as time delays, uncontrolled systems may generate instability and complexity, thereby degrading network performance. This paper provides a detailed analysis of the stability, Hopf bifurcation, and complex dynamics of a networked system under delayed feedback control. Based on the linear stability method and Hopf bifurcation theorem, the stability of the equilibrium of the error system and the existence of Hopf bifurcation are studied. The stability of periodic solutions bifurcating from the trivial equilibrium is analyzed using normal form theory and central manifold theorem. Special focus is on the effects of the network topology and time delays on the stability and Hopf bifurcation. The theoretical results are also extended to the complex networks with asymmetric adjacent matrices. In addition, the controlled model exhibits complicated dynamical behavior via three types of codimension two bifurcations and period-doubling bifurcations that eventually lead to chaos. Numerical experiments have validated the theoretical results and indicated that delayed feedback control can effectively generate or annihilate the complicated behavior of complex networks.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"16 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154244","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 Relationship Between Informal Sector and Unemployment: A Mathematical Model 非正规经济部门与失业之间的动态关系：数学模型

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500184

A. K. Misra, Mamta Kumari

{"title":"Dynamic Relationship Between Informal Sector and Unemployment: A Mathematical Model","authors":"A. K. Misra, Mamta Kumari","doi":"10.1142/s0218127424500184","DOIUrl":"https://doi.org/10.1142/s0218127424500184","url":null,"abstract":"Shortage of formal jobs, lack of skills in workforce and increasing human population proliferate the informal sector. This sector provides an opportunity to unskilled workers to gain skills along with earnings. In this paper, a deterministic nonlinear mathematical model is developed to study the effects of informal skill learning and job generation on unemployment. For the formulated system, feasibility of equilibria and their stability properties are discussed. A pertinent quantity (<math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"cal\">ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math>), known as the reproduction number, is calculated and it is shown that the formulated system undergoes transcritical, saddle-node, Hopf and Bogdanov–Takens bifurcations on the variation of <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi mathvariant=\"cal\">ℛ</mi></mrow><mrow><mn>0</mn></mrow></msub></math>. The analytically obtained results are validated through numerical simulations. The results obtained from this study indicate that a substantial rate of job generation by self-employed individuals has a stabilizing effect on the system. Moreover, self-employment along with informal skill acquisition through engaging in informal work proves to be an effective measure in curbing the issue of unemployment in society.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"16 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154126","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

Coupled HR–HNN Neuron with a Locally Active Memristor 带有局部有源 Memristor 的耦合 HR-HNN 神经元

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500226

Lili Huang, Shaotian Wang, Tengfei Lei, Keyu Huang, Chunbiao Li

{"title":"Coupled HR–HNN Neuron with a Locally Active Memristor","authors":"Lili Huang, Shaotian Wang, Tengfei Lei, Keyu Huang, Chunbiao Li","doi":"10.1142/s0218127424500226","DOIUrl":"https://doi.org/10.1142/s0218127424500226","url":null,"abstract":"Local activity could be the source for complexity. In this study, a multistable locally active memristor is proposed, whose nonvolatile memory, as well as locally active characteristics, is validated by the power-off plot and DC <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>V</mi></math>–<math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>I</mi></math> plot. Based on the two-dimensional Hindmarsh–Rose neuron and a one-dimensional Hopfield neuron, a simple neural network is constructed by connecting the two neurons with the locally active memristor. Coexisting multiple firing patterns under different initial conditions are investigated according to the controlled coupling factor. The results suggest that the system exhibits coexisting periodic and chaotic bursting with different firing patterns. Complex firing only occurs in the locally active area of the defined memristor, meanwhile the system shows a periodic oscillation in the passive area. Beyond this, the coupled neurons exhibit the specific phenomenon of attractor growing in the locally active region of the memristor. The circuit simulations by Power Simulation (PSIM) are included confirming the numerical simulations and theoretic analysis.","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":"140154049","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

Bifurcation Analysis of a Predator–Prey Model with Alternative Prey and Prey Refuges 具有备选猎物和猎物庇护所的捕食者-猎物模型的分岔分析

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500214

Wenzhe Cui, Yulin Zhao

引用次数: 0

Bifurcation Analysis of a Discrete Amensalism Model 离散 Amensalism 模型的分岔分析

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-12 DOI: 10.1142/s0218127424500202

Xinli Hu, Hanghang Li, Fengde Chen

引用次数: 0