Pub Date : 2023-06-30DOI: 10.1142/s0218127423500931
Yibo Xia, Jingwei He, Jürgen Kurths, Qinsheng Bi
We study the influence of the coexisting steady states in high-dimensional systems on the dynamical evolution of the vector field when a slow-varying periodic excitation is introduced. The model under consideration is a coupled system of Bonhöffer–van der Pol (BVP) equations with a slow-varying periodic excitation. We apply the modified slow–fast analysis method to perform a detailed study on all the equilibrium branches and their bifurcations of the generalized autonomous system. According to different dynamical behaviors, we explore the dynamical evolution of existing attractors, which reveals the coexistence of a quasi-periodic attractor with diverse types of bursting attractors. Further investigation shows that the coexisting steady states may cause spiking oscillations to behave in combination of a 2D torus and a limit cycle. We also identify a period-2 cycle bursting attractor as well as a quasi-periodic attractor according to the period-2 limit cycle.
研究了在引入慢变周期激励时，高维系统中共存稳态对矢量场动力学演化的影响。所考虑的模型是一个具有慢变周期激励的Bonhöffer-van der Pol (BVP)方程耦合系统。应用改进的慢-快分析方法对广义自治系统的所有平衡分支及其分支进行了详细的研究。根据不同的动力学行为，我们探索了现有吸引子的动力学演化，揭示了准周期吸引子与不同类型的爆发吸引子共存。进一步的研究表明，在二维环面和极限环的组合中，共存的稳态可能导致尖峰振荡。根据周期-2极限环，我们还确定了周期-2环破裂吸引子和拟周期吸引子。
{"title":"Slow-Fast Dynamics of a Coupled Oscillator with Periodic Excitation","authors":"Yibo Xia, Jingwei He, Jürgen Kurths, Qinsheng Bi","doi":"10.1142/s0218127423500931","DOIUrl":"https://doi.org/10.1142/s0218127423500931","url":null,"abstract":"We study the influence of the coexisting steady states in high-dimensional systems on the dynamical evolution of the vector field when a slow-varying periodic excitation is introduced. The model under consideration is a coupled system of Bonhöffer–van der Pol (BVP) equations with a slow-varying periodic excitation. We apply the modified slow–fast analysis method to perform a detailed study on all the equilibrium branches and their bifurcations of the generalized autonomous system. According to different dynamical behaviors, we explore the dynamical evolution of existing attractors, which reveals the coexistence of a quasi-periodic attractor with diverse types of bursting attractors. Further investigation shows that the coexisting steady states may cause spiking oscillations to behave in combination of a 2D torus and a limit cycle. We also identify a period-2 cycle bursting attractor as well as a quasi-periodic attractor according to the period-2 limit cycle.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76286792","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 : 2023-06-30DOI: 10.1142/s0218127423501006
B. Ferčec, Maja Zulj, J. Giné
In this paper, the linearizability of a [Formula: see text] resonant differential system is studied. First, we describe a method to compute the necessary conditions for linearizability based on blow-up transformation. Using the method, we compute necessary linearizability conditions for a family of [Formula: see text] resonant system with quadratic nonlinearities. The sufficiency of the obtained conditions is proven either by the Darboux linearization method or using the recursive procedure after blow-up transformation.
{"title":"Blow-Up Method for Linearizability of Resonant Differential Systems","authors":"B. Ferčec, Maja Zulj, J. Giné","doi":"10.1142/s0218127423501006","DOIUrl":"https://doi.org/10.1142/s0218127423501006","url":null,"abstract":"In this paper, the linearizability of a [Formula: see text] resonant differential system is studied. First, we describe a method to compute the necessary conditions for linearizability based on blow-up transformation. Using the method, we compute necessary linearizability conditions for a family of [Formula: see text] resonant system with quadratic nonlinearities. The sufficiency of the obtained conditions is proven either by the Darboux linearization method or using the recursive procedure after blow-up transformation.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77981412","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 : 2023-06-15DOI: 10.1142/S0218127423500827
Wei Zhou, Yuxia Liu, Rui Xue
A dynamic oligopoly game model with nonlinear cost and strategic delegation is built on the basis of isoelastic demand in this paper. And the dynamic characteristics of this game model are investigated. The local stability of the boundary equilibrium points is analyzed by means of the stability theory and Jacobian matrix, and the stability region of the Nash equilibrium point is obtained by Jury criterion. It is concluded that the system may lose stability through Flip bifurcation and Neimark–Sacker bifurcation. And the effects of speed of adjustment, price elasticity, profit weight coefficient and marginal cost on the system stability are discussed through numerical simulation. After that, the coexistence of attractors is analyzed through the basin of attraction, where multiple stability always means path dependence, implying that the long-term behavior of enterprises is strongly affected by historical contingency. In other words, a small perturbation of the initial conditions will have a significant impact on the system. In addition, the global dynamical behavior of the system is analyzed by using the critical curves, the basin of attraction, absorbing areas and a noninvertible map, revealing that three global bifurcations, the first two of which are caused by the interconversion of simply-connected and multiply-connected regions in the basin of attraction, and the third global bifurcation, that is, the final bifurcation is caused by the contact between attractors and the boundary of the basin of attraction.
{"title":"Global Dynamics of an Oligopoly Game Model with Nonlinear Costs and Strategic Delegation","authors":"Wei Zhou, Yuxia Liu, Rui Xue","doi":"10.1142/S0218127423500827","DOIUrl":"https://doi.org/10.1142/S0218127423500827","url":null,"abstract":"A dynamic oligopoly game model with nonlinear cost and strategic delegation is built on the basis of isoelastic demand in this paper. And the dynamic characteristics of this game model are investigated. The local stability of the boundary equilibrium points is analyzed by means of the stability theory and Jacobian matrix, and the stability region of the Nash equilibrium point is obtained by Jury criterion. It is concluded that the system may lose stability through Flip bifurcation and Neimark–Sacker bifurcation. And the effects of speed of adjustment, price elasticity, profit weight coefficient and marginal cost on the system stability are discussed through numerical simulation. After that, the coexistence of attractors is analyzed through the basin of attraction, where multiple stability always means path dependence, implying that the long-term behavior of enterprises is strongly affected by historical contingency. In other words, a small perturbation of the initial conditions will have a significant impact on the system. In addition, the global dynamical behavior of the system is analyzed by using the critical curves, the basin of attraction, absorbing areas and a noninvertible map, revealing that three global bifurcations, the first two of which are caused by the interconversion of simply-connected and multiply-connected regions in the basin of attraction, and the third global bifurcation, that is, the final bifurcation is caused by the contact between attractors and the boundary of the basin of attraction.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90866571","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 : 2023-06-15DOI: 10.1142/s0218127423500888
M. Katsanikas, S. Wiggins
In two previous papers [Katsanikas & Wiggins, 2021a, 2021b], we developed two methods for the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom. We applied the first method (see [Katsanikas & Wiggins, 2021a]) in the case of a quadratic Hamiltonian system in normal form with three degrees of freedom, constructing a geometrical object that is the section of a 4D toroidal structure in the 5D energy surface with the space [Formula: see text]. We provide a more detailed geometrical description of this object within the family of 4D toratopes. We proved that this object is a dividing surface and it has the no-recrossing property. In this paper, we extend the results for the case of the full 4D toroidal object in the 5D energy surface. Then we compute this toroidal object in the 5D energy surface of a coupled quadratic normal form Hamiltonian system with three degrees of freedom.
{"title":"The Generalization of the Periodic Orbit Dividing Surface for Hamiltonian Systems with Three or More Degrees of Freedom-III","authors":"M. Katsanikas, S. Wiggins","doi":"10.1142/s0218127423500888","DOIUrl":"https://doi.org/10.1142/s0218127423500888","url":null,"abstract":"In two previous papers [Katsanikas & Wiggins, 2021a, 2021b], we developed two methods for the construction of periodic orbit dividing surfaces for Hamiltonian systems with three or more degrees of freedom. We applied the first method (see [Katsanikas & Wiggins, 2021a]) in the case of a quadratic Hamiltonian system in normal form with three degrees of freedom, constructing a geometrical object that is the section of a 4D toroidal structure in the 5D energy surface with the space [Formula: see text]. We provide a more detailed geometrical description of this object within the family of 4D toratopes. We proved that this object is a dividing surface and it has the no-recrossing property. In this paper, we extend the results for the case of the full 4D toroidal object in the 5D energy surface. Then we compute this toroidal object in the 5D energy surface of a coupled quadratic normal form Hamiltonian system with three degrees of freedom.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86935578","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 : 2023-06-15DOI: 10.1142/S0218127423500815
Xin Su, Xiangjiao Shi, Liyan Geng, Renzhu Yu
Although optimization of a fresh agricultural products supply chain has been widely studied, not much attention was paid to the impact of coevolution on the stability of such a supply chain, especially in the green development of such a supply chain. In this paper, based on the synergy theory and by considering the green development of the supply chain, with logistic model deduction of the trading volume of the supply chain as the system order parameter, system dynamics simulation is performed, showing the influence of the coevolution mechanism of various subsystems and the complex evolution game process on the stability of the supply chain. These results indicate that excessive coevolution among subsystems is not conducive to the supply chain when it enters a stable and orderly state. Only when the coevolution ability is controlled within a certain range can each subsystem achieve maximum profit. At the same time, the simulation results demonstrate the positive impact of coevolution on the stability of the supply chain. Sensitivity analysis shows that environmental factors such as the recycling rate of rotten products and the levels of government regulation and environmental ethics regulation have a positive impact on the stability of the supply chain, for which the larger the climate impact factor is, the less conducive it is to the stability. This research report provides some guidance for the sustainable development of the fresh agricultural products supply chain.
{"title":"Complex Evolution Game and System Dynamics Simulation on the Impact of Coevolution on the Stability of the Fresh Agricultural Products Green Supply Chain","authors":"Xin Su, Xiangjiao Shi, Liyan Geng, Renzhu Yu","doi":"10.1142/S0218127423500815","DOIUrl":"https://doi.org/10.1142/S0218127423500815","url":null,"abstract":"Although optimization of a fresh agricultural products supply chain has been widely studied, not much attention was paid to the impact of coevolution on the stability of such a supply chain, especially in the green development of such a supply chain. In this paper, based on the synergy theory and by considering the green development of the supply chain, with logistic model deduction of the trading volume of the supply chain as the system order parameter, system dynamics simulation is performed, showing the influence of the coevolution mechanism of various subsystems and the complex evolution game process on the stability of the supply chain. These results indicate that excessive coevolution among subsystems is not conducive to the supply chain when it enters a stable and orderly state. Only when the coevolution ability is controlled within a certain range can each subsystem achieve maximum profit. At the same time, the simulation results demonstrate the positive impact of coevolution on the stability of the supply chain. Sensitivity analysis shows that environmental factors such as the recycling rate of rotten products and the levels of government regulation and environmental ethics regulation have a positive impact on the stability of the supply chain, for which the larger the climate impact factor is, the less conducive it is to the stability. This research report provides some guidance for the sustainable development of the fresh agricultural products supply chain.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83565142","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 : 2023-06-15DOI: 10.1142/S0218127423300161
Atefeh Ahmadi, S. Parthasarathy, Nikhil Pal, K. Rajagopal, S. Jafari, E. Tlelo-Cuautle
Extreme multistable systems can show vibrant dynamical properties and infinitely many coexisting attractors generated by changing the initial conditions while the system and its parameters remain unchanged. On the other hand, the frequency of extreme events in society is increasing which could have a catastrophic influence on human life worldwide. Thus, complex systems that can model such behaviors are very significant in order to avoid or control various extreme events. Also, hidden attractors are a crucial issue in nonlinear dynamics since they cannot be located and recognized with conventional methods. Hence, finding such systems is a vital task. This paper proposes a novel five-dimensional autonomous chaotic system with a line of equilibria, which generates hidden attractors. Furthermore, this system can exhibit extreme multistability and extreme events simultaneously. The fascinating features of this system are examined by dynamical analysis tools such as Poincaré sections, connecting curves, bifurcation diagrams, Lyapunov exponents spectra, and attraction basins. Moreover, the reliability of the introduced system is confirmed through analog electrical circuit design so that this chaotic circuit can be employed in many engineering fields.
{"title":"Extreme Multistability and Extreme Events in a Novel Chaotic Circuit with Hidden Attractors","authors":"Atefeh Ahmadi, S. Parthasarathy, Nikhil Pal, K. Rajagopal, S. Jafari, E. Tlelo-Cuautle","doi":"10.1142/S0218127423300161","DOIUrl":"https://doi.org/10.1142/S0218127423300161","url":null,"abstract":"Extreme multistable systems can show vibrant dynamical properties and infinitely many coexisting attractors generated by changing the initial conditions while the system and its parameters remain unchanged. On the other hand, the frequency of extreme events in society is increasing which could have a catastrophic influence on human life worldwide. Thus, complex systems that can model such behaviors are very significant in order to avoid or control various extreme events. Also, hidden attractors are a crucial issue in nonlinear dynamics since they cannot be located and recognized with conventional methods. Hence, finding such systems is a vital task. This paper proposes a novel five-dimensional autonomous chaotic system with a line of equilibria, which generates hidden attractors. Furthermore, this system can exhibit extreme multistability and extreme events simultaneously. The fascinating features of this system are examined by dynamical analysis tools such as Poincaré sections, connecting curves, bifurcation diagrams, Lyapunov exponents spectra, and attraction basins. Moreover, the reliability of the introduced system is confirmed through analog electrical circuit design so that this chaotic circuit can be employed in many engineering fields.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76542268","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 : 2023-06-15DOI: 10.1142/S0218127423300185
Xiao-Jing Li, Xiaoyuan Wang, P. Li, H. Iu, J. Eshraghian, S. K. Nandi, S. Nath, R. Elliman
We develop a tri-state memristive system based on composable binarized memristors, from both a dynamical systems construction to the development of in-house fabricated devices. Firstly, based on the SPICE model of the binary memristor, the series and parallel circuits of binary memristors are designed, and the characteristics of each circuit are analyzed in detail. Secondly, through the analysis of the connection direction and parameters of the two binary memristors, an effective method to construct a tri-state memristor is proposed, and verified using SPICE simulations. Finally, the characteristics of the constructed equivalent tri-state memristor are analyzed, and it is concluded that the amplitude, frequency and type of the input signal can affect the characteristics of the equivalent tri-state memristor. Predictions from this modeling were validated experimentally using Au/[Formula: see text]/Nb cross-point devices.
{"title":"Tri-State Memristors Based on Composable Discrete Devices","authors":"Xiao-Jing Li, Xiaoyuan Wang, P. Li, H. Iu, J. Eshraghian, S. K. Nandi, S. Nath, R. Elliman","doi":"10.1142/S0218127423300185","DOIUrl":"https://doi.org/10.1142/S0218127423300185","url":null,"abstract":"We develop a tri-state memristive system based on composable binarized memristors, from both a dynamical systems construction to the development of in-house fabricated devices. Firstly, based on the SPICE model of the binary memristor, the series and parallel circuits of binary memristors are designed, and the characteristics of each circuit are analyzed in detail. Secondly, through the analysis of the connection direction and parameters of the two binary memristors, an effective method to construct a tri-state memristor is proposed, and verified using SPICE simulations. Finally, the characteristics of the constructed equivalent tri-state memristor are analyzed, and it is concluded that the amplitude, frequency and type of the input signal can affect the characteristics of the equivalent tri-state memristor. Predictions from this modeling were validated experimentally using Au/[Formula: see text]/Nb cross-point devices.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78945949","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 : 2023-06-15DOI: 10.1142/S0218127423500876
Zhan-Ping Ma, Zhibo Cheng, Wei Liang
In this paper, we study a delayed host-generalist parasitoid diffusion model subject to homogeneous Dirichlet boundary conditions, where generalist parasitoids are introduced to control the invasion of the hosts. We construct an explicit expression of positive steady-state solution using the implicit function theorem and prove its linear stability. Moreover, by applying feedback time delay [Formula: see text] as the bifurcation parameter, spatially inhomogeneous Hopf bifurcation near the positive steady-state solution is proved when [Formula: see text] is varied through a sequence of critical values. This finding implies that feedback time delay can induce spatially inhomogeneous periodic oscillatory patterns. The direction of spatially inhomogeneous Hopf bifurcation is forward when parameter [Formula: see text] is sufficiently large. We present numerical simulations and solutions to further illustrate our main theoretical results. Numerical simulations show that the period and amplitude of the inhomogeneous periodic solution increase with increasing feedback time delay. Our theoretical analysis results only hold for parameter [Formula: see text] when it is sufficiently close to 1, whereas numerical simulations suggest that spatially inhomogeneous Hopf bifurcation still occurs when [Formula: see text] is larger than 1 but not sufficiently close to 1.
{"title":"Spatiotemporal Patterns of a Host-Generalist Parasitoid Reaction-Diffusion Model","authors":"Zhan-Ping Ma, Zhibo Cheng, Wei Liang","doi":"10.1142/S0218127423500876","DOIUrl":"https://doi.org/10.1142/S0218127423500876","url":null,"abstract":"In this paper, we study a delayed host-generalist parasitoid diffusion model subject to homogeneous Dirichlet boundary conditions, where generalist parasitoids are introduced to control the invasion of the hosts. We construct an explicit expression of positive steady-state solution using the implicit function theorem and prove its linear stability. Moreover, by applying feedback time delay [Formula: see text] as the bifurcation parameter, spatially inhomogeneous Hopf bifurcation near the positive steady-state solution is proved when [Formula: see text] is varied through a sequence of critical values. This finding implies that feedback time delay can induce spatially inhomogeneous periodic oscillatory patterns. The direction of spatially inhomogeneous Hopf bifurcation is forward when parameter [Formula: see text] is sufficiently large. We present numerical simulations and solutions to further illustrate our main theoretical results. Numerical simulations show that the period and amplitude of the inhomogeneous periodic solution increase with increasing feedback time delay. Our theoretical analysis results only hold for parameter [Formula: see text] when it is sufficiently close to 1, whereas numerical simulations suggest that spatially inhomogeneous Hopf bifurcation still occurs when [Formula: see text] is larger than 1 but not sufficiently close to 1.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83242345","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 : 2023-06-15DOI: 10.1142/S0218127423500773
Zhong Luo, Zijian Liu, Yuanshun Tan
In this paper, we propose and analyze an age-structured tumor immune model with time delay. We divide immune cells into two kinds. One is those whose growth is independent of tumor and the other is those whose growth depends on the simulation of the tumor. For these cells, their physiological ages are considered. A mature time delay [Formula: see text] is introduced to the tumor-simulation-dependent immune cells to restrict those cells who participate in the immune response to grow to a minimum physiological age. The existence and stability threshold [Formula: see text] is established for the tumor-free equilibrium state. If [Formula: see text], the tumor-free equilibrium state is both locally and globally asymptotically stable. Whereas, when [Formula: see text], the tumor equilibrium state is locally asymptotically stable if [Formula: see text] and a Hopf bifurcation occurs when [Formula: see text] passes through the threshold [Formula: see text]. This may partly explain the periodic recurrence of some tumors. Finally, theoretical results are verified by some numerical simulations.
{"title":"Stability and Hopf Bifurcation Analysis for an Age-Structured Tumor Immune Model with Time Delay","authors":"Zhong Luo, Zijian Liu, Yuanshun Tan","doi":"10.1142/S0218127423500773","DOIUrl":"https://doi.org/10.1142/S0218127423500773","url":null,"abstract":"In this paper, we propose and analyze an age-structured tumor immune model with time delay. We divide immune cells into two kinds. One is those whose growth is independent of tumor and the other is those whose growth depends on the simulation of the tumor. For these cells, their physiological ages are considered. A mature time delay [Formula: see text] is introduced to the tumor-simulation-dependent immune cells to restrict those cells who participate in the immune response to grow to a minimum physiological age. The existence and stability threshold [Formula: see text] is established for the tumor-free equilibrium state. If [Formula: see text], the tumor-free equilibrium state is both locally and globally asymptotically stable. Whereas, when [Formula: see text], the tumor equilibrium state is locally asymptotically stable if [Formula: see text] and a Hopf bifurcation occurs when [Formula: see text] passes through the threshold [Formula: see text]. This may partly explain the periodic recurrence of some tumors. Finally, theoretical results are verified by some numerical simulations.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83807465","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 : 2023-06-15DOI: 10.1142/S0218127423500803
Q. Lai, Liang Yang
This paper proposes a simple ring memristive neural network (MNN) with self-connection, bidirectional connection and a single memristive synapse. Compared with some existing MNNs, the most distinctive feature of the proposed MNN is that it can generate heterogeneous coexisting attractors and large-scale amplitude control. Various kinds of heterogeneous coexisting attractors are numerically found in the MNN, including chaos with a stable point, chaos with a limit cycle, a limit cycle with a stable point. By increasing the parameter values, the chaotic variables of the MNN can be accordingly increased and their corresponding areas are extremely wide, yielding parameter-dependent large-scale amplitude control. A circuit implementation platform is established and the obtained results demonstrate its validity and reliability.
{"title":"Heterogeneous Coexisting Attractors and Large-Scale Amplitude Control in a Simple Memristive Neural Network","authors":"Q. Lai, Liang Yang","doi":"10.1142/S0218127423500803","DOIUrl":"https://doi.org/10.1142/S0218127423500803","url":null,"abstract":"This paper proposes a simple ring memristive neural network (MNN) with self-connection, bidirectional connection and a single memristive synapse. Compared with some existing MNNs, the most distinctive feature of the proposed MNN is that it can generate heterogeneous coexisting attractors and large-scale amplitude control. Various kinds of heterogeneous coexisting attractors are numerically found in the MNN, including chaos with a stable point, chaos with a limit cycle, a limit cycle with a stable point. By increasing the parameter values, the chaotic variables of the MNN can be accordingly increased and their corresponding areas are extremely wide, yielding parameter-dependent large-scale amplitude control. A circuit implementation platform is established and the obtained results demonstrate its validity and reliability.","PeriodicalId":13688,"journal":{"name":"Int. J. Bifurc. Chaos","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85763617","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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