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

Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control 具有状态相关延迟脉冲控制的分数阶非线性系统的有限时间同步化

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500342

P. Gokul, S. S. Mohanrasu, A. Kashkynbayev, R. Rakkiyappan

{"title":"Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control","authors":"P. Gokul, S. S. Mohanrasu, A. Kashkynbayev, R. Rakkiyappan","doi":"10.1142/s0218127424500342","DOIUrl":"https://doi.org/10.1142/s0218127424500342","url":null,"abstract":"This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua’s circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm’s robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"44 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124780","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

The Effects of Negative Regulation on the Dynamical Transition in Epileptic Network 负调控对癫痫网络动态转变的影响

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s021812742450038x

Songan Hou, Haodong Wang, Denggui Fan, Ying Yu, Qingyun Wang

引用次数: 0

Bifurcations of Sliding Heteroclinic Cycles in Three-Dimensional Filippov Systems 三维菲利波夫系统中滑动异次元循环的分岔

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI: 10.1142/s0218127424500354

Yousu Huang, Qigui Yang

{"title":"Bifurcations of Sliding Heteroclinic Cycles in Three-Dimensional Filippov Systems","authors":"Yousu Huang, Qigui Yang","doi":"10.1142/s0218127424500354","DOIUrl":"https://doi.org/10.1142/s0218127424500354","url":null,"abstract":"Global bifurcations with sliding have rarely been studied in three-dimensional piecewise smooth systems. In this paper, codimension-2 bifurcations of nondegenerate sliding heteroclinic cycle <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi></math> are investigated in three-dimensional Filippov systems. Two cases of sliding heteroclinic cycle are discussed: <math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">)</mo></math> connecting two saddle-foci, <math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">)</mo></math> connecting one saddle-focus and one saddle. It is proved that at most one sliding homoclinic or one sliding periodic orbit can bifurcate from <math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Γ</mi></math> under certain conditions at the eigenvalues of the equilibria, but they cannot coexist. The asymptotic stability of the sliding periodic orbit and the structural feature of the bifurcation curves of homoclinic orbits are further studied. Finally, two numerical examples corresponding to cases <math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">)</mo></math> and <math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msub><mo stretchy=\"false\">)</mo></math>, respectively, are simulated to verify the theoretical results.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"35 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129721","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

Infinitely Many Coexisting Attractors and Scrolls in a Fractional-Order Discrete Neuron Map 分数阶离散神经元图谱中的无限多共存吸引子和卷轴

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501973

Lujie Ren, Lei Qin, Hadi Jahanshahi, Jun Mou

引用次数: 0

The Extended 16th Hilbert Problem for Discontinuous Piecewise Systems Formed by Linear Centers and Linear Hamiltonian Saddles Separated by a Nonregular Line 由线性中心和线性哈密顿鞍构成的、被非规则线分隔的不连续片断系统的扩展第 16 希尔伯特问题

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501961

Jaume Llibre, C. Valls

引用次数: 0

Impact of Allee Effect on the Spatio-Temporal Behavior of a Diffusive Epidemic Model in Heterogenous Environment 阿利效应对异质环境中扩散流行病模型时空行为的影响

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501948

Sattwika Acharya, R. K. Upadhyay, Bapin Mondal

{"title":"Impact of Allee Effect on the Spatio-Temporal Behavior of a Diffusive Epidemic Model in Heterogenous Environment","authors":"Sattwika Acharya, R. K. Upadhyay, Bapin Mondal","doi":"10.1142/s0218127423501948","DOIUrl":"https://doi.org/10.1142/s0218127423501948","url":null,"abstract":"In the current study, we have formulated an [Formula: see text] epidemic model incorporating the influence of Allee effect on the dynamics of the model system in space and time. During the spread of the disease, inhibition among the susceptible and infected individuals is seen, which is measured using the Crowley–Martin type incidence function. Extensive analysis explores the system’s stability and different bifurcation scenarios, including Hopf, saddle-node, transcritical, and Bogdanov–Takens. We also examine how these bifurcations react to parameter variations within the proposed model. The temporal model has further been extended to a spatial one to investigate the impact of the Allee effect on the formation of patterns for different values of the cross-diffusion coefficient. The well-posedness of the stationary solution and the global stability of the spatial system are derived. Also, the Turing instability, Hopf, and Turing bifurcation are calculated considering the transmission rate as critical parameter. In a heterogeneous environment, the spatial distribution of the susceptible population shows a complex structure with flat tabular surface and a few almost circular holes in surface plots for both strong and weak Allee effects. To further explore the role of Allee effect on pattern development for various cross-diffusion coefficient values, the temporal model has been spatially extended. Additionally, the transmission rate is taken into account while calculating the Turing instability and Hopf and Turing bifurcations. We ran numerical simulations to validate our analytical results for both spatial and nonspatial models. Our current model system can explain the recent occurrence of respiratory distress syndrome in endangered penguin species.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 5","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139138261","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

Chaotic Multiple-Image Encryption Algorithm Based on Block Scrambling and Dynamic DNA Coding 基于块扰码和动态 DNA 编码的混沌多图像加密算法

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501900

Xiaoyang Chen, Jun Mou, Yinghong Cao, Santo Banerjee

引用次数: 0

Chaotic Model of Muscle and Joint Interactions Based on CPG for Rehabilitation of Incomplete Spinal Cord Injury Patients 基于 CPG 的肌肉与关节相互作用混沌模型用于不完全脊髓损伤患者的康复治疗

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501894

Monireh Maleki, F. N. Rahatabad, Majid Pouladian

{"title":"Chaotic Model of Muscle and Joint Interactions Based on CPG for Rehabilitation of Incomplete Spinal Cord Injury Patients","authors":"Monireh Maleki, F. N. Rahatabad, Majid Pouladian","doi":"10.1142/s0218127423501894","DOIUrl":"https://doi.org/10.1142/s0218127423501894","url":null,"abstract":"The aim of modeling musculoskeletal systems is to understand the mechanisms of locomotion control in terms of neurophysiology and neuroanatomy. The complexity and unique nature of neuromuscular systems, however, make control problems in these systems very challenging due to several characteristics including speed and precision. Thus, their investigation requires the use of simple and analyzable methods. Consequently, taking into account the central pattern generator’s (CPG) function, we attempted to create a structured chaotic model of how human joints and muscles interact for the purpose of facilitating gait and rehabilitation in patients with incomplete spinal cord injury. The four muscle groups used in this model are gluteus, and hip flexor groups for flexion and extension of the hip joints as well as hamstring muscles and vasti muscles for flexion and extension of the knee joint. The results indicate that the output of the chaotic model of muscle and joint interactions in a healthy state would be chaotic, while in the incomplete spinal cord injury state, it would remain a fixed point. For model rehabilitation, afferent nerve stimulation is used in a CPG model; based on the modeling results, by applying coefficients of 1.98, 2.21, and 3.1 to the values of Ia, II, and Ib afferent nerves, the incomplete spinal cord injury model state is changed from a fix-point to periodic in a permanent fashion, suggesting locomotion with rehabilitation in our model. Based on the results obtained from the chaotic model of muscle and joint interactions as well as the comparisons made with reference papers, it can be stated that this model has acceptable output while enjoying simple computations and can predict different norms.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 13","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139137739","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

Complex Dynamics and Fractional-Order Optimal Control of an Epidemic Model with Saturated Treatment and Incidence 具有饱和治疗和发病率的流行病模型的复杂动力学和分数阶最优控制

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501924

Suvankar Majee, T. K. Kar, Soovoojeet Jana, D. K. Das, J. J. Nieto

{"title":"Complex Dynamics and Fractional-Order Optimal Control of an Epidemic Model with Saturated Treatment and Incidence","authors":"Suvankar Majee, T. K. Kar, Soovoojeet Jana, D. K. Das, J. J. Nieto","doi":"10.1142/s0218127423501924","DOIUrl":"https://doi.org/10.1142/s0218127423501924","url":null,"abstract":"In this study, we have developed a novel SIR epidemic model by incorporating fractional-order differential equations and utilizing saturated-type functions to describe both disease incidence and treatment. The intricate dynamical characteristics of the proposed model, encompassing the determination of the conditions for the existence of all possible feasible equilibria with their local and global stability criteria, are investigated thoroughly. The model undergoes backward bifurcation with respect to the parameter representing the side effects due to treatment. This phenomenon emphasizes the critical role of treatment control parameters in shaping epidemic outcomes. In addition, to understand the optimal role of the treatment in mitigating the disease prevalence and minimizing the associated cost, we investigated a fractional-order optimal control problem. To further visualize the analytical results, we have conducted simulation works considering feasible parameter values for the model. Finally, we have employed local and global sensitivity analysis techniques to identify the factors that have the greatest potential to reduce the impact of the disease.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 17","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139138198","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

Ultra-Chaos in the Motion of Walking Droplet 行走水滴运动中的超混沌现象

IF 2.2 4区数学

International Journal of Bifurcation and Chaos Pub Date : 2023-12-30 DOI: 10.1142/s0218127423501912

Yu Yang, Shijie Qin, Shijun Liao

{"title":"Ultra-Chaos in the Motion of Walking Droplet","authors":"Yu Yang, Shijie Qin, Shijun Liao","doi":"10.1142/s0218127423501912","DOIUrl":"https://doi.org/10.1142/s0218127423501912","url":null,"abstract":"A liquid bath vibrating vertically can lead to the emergence of a self-propelled walking droplet on its free surface, which can exhibit chaotic motion. It is well-known that trajectories of a chaotic system are sensitive to its initial condition, known as the “butterfly-effect”, while its statistics normally remain stable to small disturbances: this type of chaos is called “normal-chaos”. However, a concept called “ultra-chaos” has been recently introduced, whose statistical features are unstable, i.e. extremely sensitive to small disturbances. Up to now, a few examples of ultra-chaos have been reported. In this paper, the influence of tiny disturbances on the motion of walking droplet is investigated. It is found that both normal-chaos and ultra-chaos exist in the motion of the walking droplet. Different from the normal-chaotic motion, even the statistical properties of the droplet’s ultra-chaotic motion are sensitive to tiny disturbances. Therefore, this illustrates once again that ultra-chaos indeed exists widely and represents a higher disorder compared with normal-chaos. The ultra-chaos as a new concept can widen our knowledge about chaos and provide us with a new point of view to study chaotic properties. It should be emphasized that, for an ultra-chaos, it is impossible to repeat any results of its physical experiments or numerical simulations even in the meaning of statistics! Unfortunately, reproducibility is a corner stone of modern science. Thus, the paradigm of modern scientific research might be invalid for an ultra-chaotic system.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139140397","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