Pub Date : 2024-07-11DOI: 10.1142/s0218127424501141
Deniz Elmacı, Figen Kangalgil
This study discusses the dynamic behaviors of the prey–predator model subject to the Allee effect and the harvesting of prey species. The existence of fixed points and the topological categorization of the co-existing fixed point of the model are determined. It is shown that the discrete-time prey–predator model can undergo Flip and Neimark–Sacker bifurcations under some parametric assumptions using bifurcation theory and the center manifold theorem. A chaos control technique called the feedback-control method is utilized to eliminate chaos. Numerical examples are given to support the theoretical findings and investigate chaos strategies’ effectiveness and feasibility. Additionally, bifurcation diagrams, phase portraits, maximum Lyapunov exponents, and a graph showing chaos control are demonstrated.
{"title":"Complex Dynamics of a Discrete Prey–Predator Model Exposing to Harvesting and Allee Effect on the Prey Species with Chaos Control","authors":"Deniz Elmacı, Figen Kangalgil","doi":"10.1142/s0218127424501141","DOIUrl":"https://doi.org/10.1142/s0218127424501141","url":null,"abstract":"This study discusses the dynamic behaviors of the prey–predator model subject to the Allee effect and the harvesting of prey species. The existence of fixed points and the topological categorization of the co-existing fixed point of the model are determined. It is shown that the discrete-time prey–predator model can undergo Flip and Neimark–Sacker bifurcations under some parametric assumptions using bifurcation theory and the center manifold theorem. A chaos control technique called the feedback-control method is utilized to eliminate chaos. Numerical examples are given to support the theoretical findings and investigate chaos strategies’ effectiveness and feasibility. Additionally, bifurcation diagrams, phase portraits, maximum Lyapunov exponents, and a graph showing chaos control are demonstrated.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"14 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141656181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-08DOI: 10.1142/s0218127424501086
Zhouyu Hu, Zikun Han, Yanling Yang, Qiubao Wang
In this paper, we study a class of nonlinear stochastic Duffing oscillators with multidelay feedback. We propose an effective reduction approach with the help of center manifold theory and stochastic averaging method. Taking the initial time-delay [Formula: see text] as the parameter, we reduce the original system to a one-dimensional averaged Itô equation. Our analysis reveals that the original system exhibits stochastic bifurcations, including stochastic D and P bifurcations. Once we have a clear understanding of the bifurcation structure, we can use this knowledge to choose appropriate system parameters and place the system in the desired state. For instance, by adjusting the initial time-delay [Formula: see text] of the control system, we can stabilize the system and achieve the desired outcome. Numerical simulations also verify the theoretical results. With appropriate parameter choices, multiple time delays can destabilize the equilibrium and promote chaotic behaviors, and can also lead to more stable dynamical behavior. Remarkably, we discovered that increasing the interval of time delays and feedback numbers can enhance system stability. It may potentially serve as a novel mechanism for stabilizing stochastic systems. The study provides a solid theoretical foundation for exploring stochastic systems subject to complex time-delay feedback control, and offers a valuable framework for related fields.
本文研究了一类具有多期反馈的非线性随机达芬振荡器。我们借助中心流形理论和随机平均法，提出了一种有效的还原方法。以初始时延[公式：见正文]为参数，我们将原系统还原为一维平均伊托方程。我们的分析表明，原系统呈现随机分岔，包括随机 D 分岔和随机 P 分岔。一旦我们对分岔结构有了清晰的了解，就可以利用这些知识选择适当的系统参数，将系统置于所需的状态。例如，通过调整控制系统的初始时延[计算公式：见正文]，我们可以稳定系统并达到预期结果。数值模拟也验证了理论结果。在参数选择适当的情况下，多重时间延迟可以破坏平衡并促进混乱行为，也可以带来更稳定的动态行为。值得注意的是，我们发现增加时间延迟和反馈次数的间隔可以增强系统的稳定性。这有可能成为稳定随机系统的一种新机制。这项研究为探索复杂时延反馈控制的随机系统提供了坚实的理论基础，并为相关领域提供了有价值的框架。
{"title":"Combined Impact of Multidelay Feedback Number and Interval: A Novel Mechanism for Controlling the Stability of Stochastic Duffing Systems","authors":"Zhouyu Hu, Zikun Han, Yanling Yang, Qiubao Wang","doi":"10.1142/s0218127424501086","DOIUrl":"https://doi.org/10.1142/s0218127424501086","url":null,"abstract":"In this paper, we study a class of nonlinear stochastic Duffing oscillators with multidelay feedback. We propose an effective reduction approach with the help of center manifold theory and stochastic averaging method. Taking the initial time-delay [Formula: see text] as the parameter, we reduce the original system to a one-dimensional averaged Itô equation. Our analysis reveals that the original system exhibits stochastic bifurcations, including stochastic D and P bifurcations. Once we have a clear understanding of the bifurcation structure, we can use this knowledge to choose appropriate system parameters and place the system in the desired state. For instance, by adjusting the initial time-delay [Formula: see text] of the control system, we can stabilize the system and achieve the desired outcome. Numerical simulations also verify the theoretical results. With appropriate parameter choices, multiple time delays can destabilize the equilibrium and promote chaotic behaviors, and can also lead to more stable dynamical behavior. Remarkably, we discovered that increasing the interval of time delays and feedback numbers can enhance system stability. It may potentially serve as a novel mechanism for stabilizing stochastic systems. The study provides a solid theoretical foundation for exploring stochastic systems subject to complex time-delay feedback control, and offers a valuable framework for related fields.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 1117","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141668829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-05DOI: 10.1142/s0218127424501177
Tianhao Zhao, Yue Zhou, Xiaofang Hu
Speech Emotion Recognition (SER) is a challenging task characterized by the diversity and complexity of emotional expression. Due to its powerful feature extraction capabilities, Transformer Network (TN) demonstrates advantages and potential in SER. However, the limited size of available datasets and the difficulty of decoupling emotional features restrain its performance and present challenges in implementing SER on edge devices. To address these issues, we present a Memristor-based Progressive Hierarchical Conformer Architecture (MPCA) and design a conformer submodule that leverages convolution to mitigate TN’s limitations in SER. We propose attention-based feature decoupling, employing hierarchical extraction to decouple speaker characteristics and retain the relevant components, thereby obtaining reliable emotional features. Furthermore, we propose a reconfigurable circuit implementation scheme for MPCA based on operator multiplexing achieving flexible modules that can be dynamically adjusted based on the resources of edge devices, and the stability of the designed circuit is analyzed by simulation experiments with PSPICE. We show that the suggested MPCA demonstrates state-of-the-art performance in SER while significantly reducing system power consumption, offering a solution for SER implementation on edge devices.
语音情感识别（SER）是一项具有挑战性的任务，其特点是情感表达的多样性和复杂性。变压器网络（TN）具有强大的特征提取能力，因此在 SER 中显示出优势和潜力。然而，可用数据集的规模有限以及情感特征解耦的难度限制了它的性能，也给在边缘设备上实施 SER 带来了挑战。为了解决这些问题，我们提出了基于 Memristor 的渐进式分层构形器架构 (MPCA)，并设计了一个构形器子模块，利用卷积来缓解 TN 在 SER 中的局限性。我们提出了基于注意力的特征解耦，利用分层提取来解耦说话者特征并保留相关成分，从而获得可靠的情感特征。此外，我们还提出了基于算子复用的 MPCA 可重构电路实现方案，实现了可根据边缘设备资源动态调整的灵活模块，并通过 PSPICE 仿真实验分析了所设计电路的稳定性。我们通过 PSPICE 仿真实验分析了所设计电路的稳定性，结果表明，所建议的 MPCA 在大幅降低系统功耗的同时，还展示了最先进的 SER 性能，为在边缘设备上实现 SER 提供了一种解决方案。
{"title":"Memristor-Based Progressive Hierarchical Conformer Architecture for Speech Emotion Recognition","authors":"Tianhao Zhao, Yue Zhou, Xiaofang Hu","doi":"10.1142/s0218127424501177","DOIUrl":"https://doi.org/10.1142/s0218127424501177","url":null,"abstract":"Speech Emotion Recognition (SER) is a challenging task characterized by the diversity and complexity of emotional expression. Due to its powerful feature extraction capabilities, Transformer Network (TN) demonstrates advantages and potential in SER. However, the limited size of available datasets and the difficulty of decoupling emotional features restrain its performance and present challenges in implementing SER on edge devices. To address these issues, we present a Memristor-based Progressive Hierarchical Conformer Architecture (MPCA) and design a conformer submodule that leverages convolution to mitigate TN’s limitations in SER. We propose attention-based feature decoupling, employing hierarchical extraction to decouple speaker characteristics and retain the relevant components, thereby obtaining reliable emotional features. Furthermore, we propose a reconfigurable circuit implementation scheme for MPCA based on operator multiplexing achieving flexible modules that can be dynamically adjusted based on the resources of edge devices, and the stability of the designed circuit is analyzed by simulation experiments with PSPICE. We show that the suggested MPCA demonstrates state-of-the-art performance in SER while significantly reducing system power consumption, offering a solution for SER implementation on edge devices.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141675497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-05DOI: 10.1142/s0218127424501098
Hailong Yuan, You Zhou, Xiaoyi Yang, Yang Lv, Gaihui Guo
This paper is concerned with a spatial [Formula: see text] epidemic model with nonlinear incidence rate. First, the existence of the equilibrium is discussed in different conditions. Then the main criteria for the stability and instability of the constant steady-state solutions are presented. In addition, the effect of diffusion coefficients on Turing instability is described. Next, by applying the normal form theory and the center manifold theorem, the existence and direction of Hopf bifurcation for the ordinary differential equations system and the partial differential equations system are given, respectively. The bifurcation diagrams of Hopf and Turing bifurcations are shown. Moreover, a priori estimates and local steady-state bifurcation are investigated. Furthermore, our analysis focuses on providing specific conditions that can determine the local bifurcation direction and extend the local bifurcation to the global one. Finally, the numerical results demonstrate that the intrinsic growth rate, denoted as [Formula: see text], has significant influence on the spatial pattern. Specifically, different patterns appear, with the increase of [Formula: see text]. The obtained results greatly expand on the discovery of pattern formation in the epidemic model.
{"title":"Bifurcation and Instability of a Spatial Epidemic Model","authors":"Hailong Yuan, You Zhou, Xiaoyi Yang, Yang Lv, Gaihui Guo","doi":"10.1142/s0218127424501098","DOIUrl":"https://doi.org/10.1142/s0218127424501098","url":null,"abstract":"This paper is concerned with a spatial [Formula: see text] epidemic model with nonlinear incidence rate. First, the existence of the equilibrium is discussed in different conditions. Then the main criteria for the stability and instability of the constant steady-state solutions are presented. In addition, the effect of diffusion coefficients on Turing instability is described. Next, by applying the normal form theory and the center manifold theorem, the existence and direction of Hopf bifurcation for the ordinary differential equations system and the partial differential equations system are given, respectively. The bifurcation diagrams of Hopf and Turing bifurcations are shown. Moreover, a priori estimates and local steady-state bifurcation are investigated. Furthermore, our analysis focuses on providing specific conditions that can determine the local bifurcation direction and extend the local bifurcation to the global one. Finally, the numerical results demonstrate that the intrinsic growth rate, denoted as [Formula: see text], has significant influence on the spatial pattern. Specifically, different patterns appear, with the increase of [Formula: see text]. The obtained results greatly expand on the discovery of pattern formation in the epidemic model.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141676397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-05DOI: 10.1142/s0218127424300192
Tiantian Wu, Zhe Zhao, Songmei Huan
This paper studies sliding homoclinic bifurcations in a class of symmetric three-zone three-dimensional piecewise affine systems. The systems have one parameter and the unperturbed systems have a pair of sliding homoclinic orbits to a saddle. Based on the analysis of the one-dimensional Poincaré maps, two types of sliding cycles are obtained from the sliding homoclinic bifurcations of the systems. In addition, two examples of sliding homoclinic orbits and sliding cycles are provided with simulations to illustrate the effectiveness of the theorems.
{"title":"Sliding Homoclinic Bifurcations in a Class of Three-Dimensional Piecewise Affine Systems","authors":"Tiantian Wu, Zhe Zhao, Songmei Huan","doi":"10.1142/s0218127424300192","DOIUrl":"https://doi.org/10.1142/s0218127424300192","url":null,"abstract":"This paper studies sliding homoclinic bifurcations in a class of symmetric three-zone three-dimensional piecewise affine systems. The systems have one parameter and the unperturbed systems have a pair of sliding homoclinic orbits to a saddle. Based on the analysis of the one-dimensional Poincaré maps, two types of sliding cycles are obtained from the sliding homoclinic bifurcations of the systems. In addition, two examples of sliding homoclinic orbits and sliding cycles are provided with simulations to illustrate the effectiveness of the theorems.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 48","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141673445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-03DOI: 10.1142/s0218127424501165
A. K. Misra, Mamta Kumari
The limited availability of formal jobs in developing nations always heightens the challenge for unemployed individuals in securing regular employment. Temporary employment in the informal sector serves as a source to fulfill their basic needs and enhance their employable skills. In this paper, we introduce a nonlinear mathematical model to study the effect of informal and formal jobs on the dynamics of unemployment. For the model formulation, we categorize the labor force into three classes: unemployed, temporary employed, and regularly employed. A separate dynamical variable is used to represent the available temporary vacancies. It is assumed that temporarily employed individuals may transition into regular employment or self-employment. Furthermore, self-employed individuals contribute to generating temporary vacancies within the informal sector. The long-term behavior of the proposed system is analyzed using the qualitative theory of differential equations. A quantity known as the reproduction number of the system is derived, and it is found that the occurrence of multiple bifurcations for the proposed system is influenced by the value of this threshold quantity. Furthermore, we validate our analytical findings numerically. The findings of this study illustrate that an increase in the shifting rate of individuals from temporary to regular employment is not always effective in increasing the number of regularly employed individuals. Additionally, an increase in the transition of temporarily employed individuals into self-employment, coupled with their involvement in creating more temporary jobs, proves beneficial in reducing unemployment.
{"title":"Modeling the Effect of Informal and Formal Jobs on the Dynamics of Unemployment","authors":"A. K. Misra, Mamta Kumari","doi":"10.1142/s0218127424501165","DOIUrl":"https://doi.org/10.1142/s0218127424501165","url":null,"abstract":"The limited availability of formal jobs in developing nations always heightens the challenge for unemployed individuals in securing regular employment. Temporary employment in the informal sector serves as a source to fulfill their basic needs and enhance their employable skills. In this paper, we introduce a nonlinear mathematical model to study the effect of informal and formal jobs on the dynamics of unemployment. For the model formulation, we categorize the labor force into three classes: unemployed, temporary employed, and regularly employed. A separate dynamical variable is used to represent the available temporary vacancies. It is assumed that temporarily employed individuals may transition into regular employment or self-employment. Furthermore, self-employed individuals contribute to generating temporary vacancies within the informal sector. The long-term behavior of the proposed system is analyzed using the qualitative theory of differential equations. A quantity known as the reproduction number of the system is derived, and it is found that the occurrence of multiple bifurcations for the proposed system is influenced by the value of this threshold quantity. Furthermore, we validate our analytical findings numerically. The findings of this study illustrate that an increase in the shifting rate of individuals from temporary to regular employment is not always effective in increasing the number of regularly employed individuals. Additionally, an increase in the transition of temporarily employed individuals into self-employment, coupled with their involvement in creating more temporary jobs, proves beneficial in reducing unemployment.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"35 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-03DOI: 10.1142/s0218127424501189
Yiren Chen, Yan Liang, Xuefeng Gao, Si Chen, Yu Han
We investigate novel bifurcation phenomena in the generalized KdV–mKdV-like equation. Unlike previous phase diagram studies, we choose variables related to wave speed as the coordinate axis, which led us to discover some interesting bifurcation phenomena. Our method can also be extended to study some other bifurcation phenomena in equations.
{"title":"Some Interesting Bifurcation Phenomena in the Generalized KdV–mKdV-Like Equation","authors":"Yiren Chen, Yan Liang, Xuefeng Gao, Si Chen, Yu Han","doi":"10.1142/s0218127424501189","DOIUrl":"https://doi.org/10.1142/s0218127424501189","url":null,"abstract":"We investigate novel bifurcation phenomena in the generalized KdV–mKdV-like equation. Unlike previous phase diagram studies, we choose variables related to wave speed as the coordinate axis, which led us to discover some interesting bifurcation phenomena. Our method can also be extended to study some other bifurcation phenomena in equations.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"75 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141682360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-03DOI: 10.1142/s0218127424501116
Xiao-Long Gao, Zhiyuan Li, Yu-Lan Wang
The establishment of a financial system should not only consider the current situation, but also need to refer to the past. Due to the memory of the fractional derivative, a fractional-order system can more effectively describe the historical significance of the financial system. Most scholars use the prediction–correction scheme to study fractional-order systems. This paper provides a higher-precision numerical method for the financial system, which more effectively simulate the system. Based on the definition of the Grünwald–Letnikov fractional derivative, the integer-order system with nonconstant demand elasticity is extended to the fractional-order setting, and its dynamic behavior is studied, with some novel chaotic attractors found. The research results are helpful for improving the understanding of the financial system and the financial market and for predicting financial risks.
{"title":"Chaotic Dynamic Behavior of a Fractional-Order Financial System with Constant Inelastic Demand","authors":"Xiao-Long Gao, Zhiyuan Li, Yu-Lan Wang","doi":"10.1142/s0218127424501116","DOIUrl":"https://doi.org/10.1142/s0218127424501116","url":null,"abstract":"The establishment of a financial system should not only consider the current situation, but also need to refer to the past. Due to the memory of the fractional derivative, a fractional-order system can more effectively describe the historical significance of the financial system. Most scholars use the prediction–correction scheme to study fractional-order systems. This paper provides a higher-precision numerical method for the financial system, which more effectively simulate the system. Based on the definition of the Grünwald–Letnikov fractional derivative, the integer-order system with nonconstant demand elasticity is extended to the fractional-order setting, and its dynamic behavior is studied, with some novel chaotic attractors found. The research results are helpful for improving the understanding of the financial system and the financial market and for predicting financial risks.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":"26 S75","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141683407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-07DOI: 10.1142/s0218127424500901
Xin-You Meng, Li Xiao
In this paper, a diffusive zooplankton–phytoplankton model with time delay and hunting cooperation is established. First, the existence of all positive equilibria and their local stability are proved when the system does not include time delay and diffusion. Then, the existence of Hopf bifurcation at the positive equilibrium is proved by taking time delay as the bifurcation parameter, and the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are investigated by using the center manifold theorem and the normal form theory in partial differential equations. Next, according to the theory of Turing bifurcation, the conditions for the occurrence of Turing bifurcation are obtained by taking the intraspecific competition rate of the prey as the bifurcation parameter. Furthermore, the corresponding amplitude equations are discussed by using the standard multi-scale analysis method. Finally, some numerical simulations are given to verify the theoretical results.
{"title":"Hopf Bifurcation and Turing Instability of a Delayed Diffusive Zooplankton–Phytoplankton Model with Hunting Cooperation","authors":"Xin-You Meng, Li Xiao","doi":"10.1142/s0218127424500901","DOIUrl":"https://doi.org/10.1142/s0218127424500901","url":null,"abstract":"In this paper, a diffusive zooplankton–phytoplankton model with time delay and hunting cooperation is established. First, the existence of all positive equilibria and their local stability are proved when the system does not include time delay and diffusion. Then, the existence of Hopf bifurcation at the positive equilibrium is proved by taking time delay as the bifurcation parameter, and the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are investigated by using the center manifold theorem and the normal form theory in partial differential equations. Next, according to the theory of Turing bifurcation, the conditions for the occurrence of Turing bifurcation are obtained by taking the intraspecific competition rate of the prey as the bifurcation parameter. Furthermore, the corresponding amplitude equations are discussed by using the standard multi-scale analysis method. Finally, some numerical simulations are given to verify the theoretical results.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141372177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the impact of the strong Allee effect and ratio-dependent Holling–Tanner functional response on the dynamical behaviors of a predator–prey system is investigated. First, the positivity and boundedness of solutions of the system are proved. Then, stability and bifurcation analysis on equilibria is provided, with explicit conditions obtained for Hopf bifurcation. Moreover, global dynamics of the system is discussed. In particular, the degenerate singular point at the origin is proved to be globally asymptotically stable under various conditions. Further, a detailed bifurcation analysis is presented to show that the system undergoes a codimension-[Formula: see text] Hopf bifurcation and a codimension-[Formula: see text] cusp Bogdanov–Takens bifurcation. Simulations are given to illustrate the theoretical predictions. The results obtained in this paper indicate that the strong Allee effect and proportional dependence coefficient have significant impact on the fundamental change of predator–prey dynamics and the species persistence.
{"title":"Local and Global Dynamics of a Ratio-Dependent Holling–Tanner Predator–Prey Model with Strong Allee Effect","authors":"Weiping Lou, Pei Yu, Jia-Fang Zhang, Claudio Arancibia-Ibarra","doi":"10.1142/s0218127424500925","DOIUrl":"https://doi.org/10.1142/s0218127424500925","url":null,"abstract":"In this paper, the impact of the strong Allee effect and ratio-dependent Holling–Tanner functional response on the dynamical behaviors of a predator–prey system is investigated. First, the positivity and boundedness of solutions of the system are proved. Then, stability and bifurcation analysis on equilibria is provided, with explicit conditions obtained for Hopf bifurcation. Moreover, global dynamics of the system is discussed. In particular, the degenerate singular point at the origin is proved to be globally asymptotically stable under various conditions. Further, a detailed bifurcation analysis is presented to show that the system undergoes a codimension-[Formula: see text] Hopf bifurcation and a codimension-[Formula: see text] cusp Bogdanov–Takens bifurcation. Simulations are given to illustrate the theoretical predictions. The results obtained in this paper indicate that the strong Allee effect and proportional dependence coefficient have significant impact on the fundamental change of predator–prey dynamics and the species persistence.","PeriodicalId":506426,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":" 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141372820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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