International Journal of Bifurcation and Chaos最新文献

{"title":"Two-Parameter Bifurcations and Hidden Attractors in a Class of 3D Linear Filippov Systems","authors":"Zhouchao Wei, Fanrui Wang","doi":"10.1142/s0218127424500524","DOIUrl":"https://doi.org/10.1142/s0218127424500524","url":null,"abstract":"<p>We take into consideration two different kinds of two-parameter bifurcations in a class of 3D linear Filippov systems, namely pseudo-Bautin bifurcation and boundary equilibrium bifurcations for two scenarios. The bifurcation conditions for generating rich dynamic behaviors are established. The main objective is to investigate the effects of two parameters interacting simultaneously on a variety of dynamic phenomena. In order to analyze the pseudo-Bautin bifurcation, we build the Poincaré map and analyze the number of fixed points whose types are related to the crossing limit cycles. In order to analyze boundary equilibrium bifurcations for two scenarios, we perform an analysis on the existence and admissibility of equilibria. Besides, a comprehensive investigation on hidden attractors induced by boundary equilibrium bifurcations is conducted. The novelty resides in overcoming the constraints of previous studies that solely take into account the dynamics of individual parameter variations. We innovatively characterize the two-parameter bifurcation mechanism of a new class of Filippov systems, and qualitatively demonstrate the coexistence of hidden attractor and stable pseudo-equilibrium.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196384","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}

{"title":"Nonlinear Dynamic Analysis and Forecasting of Symmetric Aerostatic Cavities Bearing Systems","authors":"Ta-Jen Peng, Ping-Huan Kuo, Wei-Cheng Huang, Cheng-Chi Wang","doi":"10.1142/s0218127424300088","DOIUrl":"https://doi.org/10.1142/s0218127424300088","url":null,"abstract":"<p>Symmetric Aerostatic Cavities Bearing (SACB) systems have attracted increasing attention in the field of high-precision machinery, particularly rotational mechanisms applied at ultra-high speeds. In an air bearing system, the air bearing serves as the main support, and the load-carrying capacity is not as high as that of oil film bearings. However, the aero-spindle can operate at considerably high rotational speeds with relatively lower heat generated from rotation compared with that of oil film bearings. In addition, the operating environment of air bearings does not easily cause the rotor to deform. Hence, through adequate design, air pressure systems exhibit a certain level of stability. In general, the pressure distribution function of air bearings exhibits strong nonlinearity when there are changes in the rotor mass or rotational speed, or when the bearing system is inadequately designed. These issues may lead to instabilities in the rotor, such as unpredictable nonperiodic movements, rotor collisions, or even chaotic movements under certain parameters. In this study, rotor oscillation was analyzed using the maximum Lyapunov exponent to identify whether chaotic behavior occurred. Machine learning methods were then used to establish models and predict the rotor behavior. Especially, random forest and extreme gradient boosting were combined to develop a new model and confirm whether this model offered higher prediction performance and more accurate results in predicting tendencies with considerable changes compared with other models. The results can be effectively used to predict the SACB system and prevent nonlinear behavior from occurring.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205354","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}

{"title":"Multiparameter Bifurcation Analysis of Power Systems Integrating Large-Scale Solar Photovoltaic and Wind Farms Power Plants","authors":"Abdelaziz Salah Saidi, Muneer Parayangat, Mohamed Ali Rakrouki, Saad M. Saad, Naser El Naily","doi":"10.1142/s0218127424500299","DOIUrl":"https://doi.org/10.1142/s0218127424500299","url":null,"abstract":"<p>In this paper, we propose a novel codimension-three-parameter bifurcation analysis of equilibria and limit cycles when integrating Renewable Energy Sources (RESs) power plants with an exponential static load model. The study investigates the effect of solar photovoltaic generation margin, wind power generation margin, and loading factor on the local bifurcation of the modified IEEE nine-bus system. The proposed technique considers the real case of the West System Coordination Council (WSCC), the western states of the USA, by using specific models of RES power plants and static loads. The proposed technique helps to create a set of linearly varying parameters for critical operating points of nonlinear systems. The study explores detailed voltage stability analysis through the examination of bifurcation diagrams. The Hopf, limit-induced, and saddle-node bifurcation branches are identified, defining the parameter space’s stable and unstable operational regions. Additionally, the stability regions surrounding the equilibrium points are diligently explored, clarifying the consequences that various bifurcations may exert on these regions. The study offered in this proposed work aids in determining the best ways to monitor and improve these margins while considering system variables and load design.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140196380","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}

{"title":"Weak Sensitive Compactness for Linear Operators","authors":"Quanquan Yao, Peiyong Zhu","doi":"10.1142/s0218127424500160","DOIUrl":"https://doi.org/10.1142/s0218127424500160","url":null,"abstract":"<p>Let <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></math></span><span></span> be a linear dynamical system, where <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>X</mi></math></span><span></span> is a separable Banach space and <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>T</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>X</mi></math></span><span></span> is a bounded linear operator. We show that if <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is invertible, then <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is weakly sensitive compact if and only if <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is thickly weakly sensitive compact; and that there exists a system <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo stretchy=\"false\">×</mo><mi>Y</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">×</mo><mi>S</mi><mo stretchy=\"false\">)</mo></math></span><span></span> such that:</p><table border=\"0\" list-type=\"order\" width=\"95%\"><tr><td valign=\"top\">(1)</td><td colspan=\"5\" valign=\"top\"><p><span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo stretchy=\"false\">×</mo><mi>Y</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">×</mo><mi>S</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is cofinitely weakly sensitive compact;</p></td></tr><tr><td valign=\"top\">(2)</td><td colspan=\"5\" valign=\"top\"><p><span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></math></span><span></span> and <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>Y</mi><mo>,</mo><mi>S</mi><mo stretchy=\"false\">)</mo></math></span><span></span> are weakly sensitive compact; and</p></td></tr><tr><td valign=\"top\">(3)</td><td colspan=\"5\" valign=\"top\"><p><span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>X</mi><mo>,</mo><mi>T</mi><mo stretchy=\"false\">)</mo></math></span><span></span> and <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>Y</mi><mo>,</mo><mi>S</mi><mo stretchy=\"false\">)</mo></math></span><span></span> are not syndetically weakly sensitive compact.</p></td></tr></table><p>We also show that if <span><math altimg=\"eq-00013.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154037","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}

{"title":"Impact of Fear and Group Defense on the Dynamics of a Predator–Prey System","authors":"Soumitra Pal, Sarbari Karmakar, Saheb Pal, Nikhil Pal, A. K. Misra, Joydev Chattopadhyay","doi":"10.1142/s0218127424500196","DOIUrl":"https://doi.org/10.1142/s0218127424500196","url":null,"abstract":"<p>To reduce the chance of predation, many prey species adopt group defense mechanisms. While it is commonly believed that such defense mechanisms lead to positive feedback on prey density, a closer observation reveals that it may impact the growth rate of species. This is because individuals invest more time and effort in defense rather than reproductive activities. In this study, we delve into a predator–prey system where predator-induced fear influences the birth rate of prey, and the prey species exhibit group defense mechanism. We adopt a nonmonotonic functional response to govern the predator–prey interaction, which effectively captures the group defense mechanism. We present a detailed mathematical analysis, encompassing the determination of feasible equilibria and their stability conditions. Through the analytical approach, we demonstrate the occurrence of Hopf and Bogdanov–Takens (BT) bifurcations. We observe two distinct types of bistabilities in the system: one between interior and predator-free equilibria, and another between limit cycle and predator-free equilibrium. Our findings reveal that the parameters associated with group defense and predator-induced fear play significant roles in the survival and extinction of populations.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154128","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}

{"title":"Bistability and Bifurcations of Tumor Dynamics with Immune Escape and the Chimeric Antigen Receptor T-Cell Therapy","authors":"Shaoli Wang, Tengfei Wang, Xiyan Bai, Shaoping Ji, Tianhai Tian","doi":"10.1142/s0218127424500159","DOIUrl":"https://doi.org/10.1142/s0218127424500159","url":null,"abstract":"<p>Tumor immune escape refers to the inability of the immune system to clear tumor cells, which is one of the major obstacles in designing effective treatment schemes for cancer diseases. Although clinical studies have led to promising treatment outcomes, it is imperative to design theoretical models to investigate the long-term treatment effects. In this paper, we develop a mathematical model to study the interactions among tumor cells, immune escape tumor cells, and T lymphocyte. The chimeric antigen receptor (CAR) T-cell therapy is also described by the mathematical model. Bifurcation analysis shows that there exists backward bifurcation and saddle-node bifurcation when the immune intensity is used as the bifurcation parameter. The proposed model also exhibits bistability when its parameters are located between the saddle-node threshold and backward bifurcation threshold. Sensitivity analysis is performed to illustrate the effects of different mechanisms on the backward bifurcation threshold and basic immune reproduction number. Simulation studies confirm the bifurcation analysis results and predict various types of treatment outcomes using different CAR T-cell therapy strengths. Analysis and simulation results show that the immune intensity can be used to control the tumor size, but it has no effect on the control of the immune escape tumor size. The introduction of the CAR T-cell therapy will reduce the immune escape tumor size and the treatment effect depends on the CAR T-cell therapy strength.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154129","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}

{"title":"On–Off Intermittency and Long-Term Reactivity in a Host–Parasitoid Model with a Deterministic Driver","authors":"Fasma Diele, Deborah Lacitignola, Angela Monti","doi":"10.1142/s021812742450041x","DOIUrl":"https://doi.org/10.1142/s021812742450041x","url":null,"abstract":"<p>Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host–parasitoid systems. We explore the impact of environment on the host–parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental fluctuations on the average host population growth rate. We hence focus on the discrete host–parasitoid Beddington–Free–Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on–off intermittency in host–parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on–off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on–off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154122","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}

{"title":"Stabilization of Laminars in Chaos Intermittency","authors":"Michiru Katayama, Kenji Ikeda, Tetsushi Ueta","doi":"10.1142/s021812742450024x","DOIUrl":"https://doi.org/10.1142/s021812742450024x","url":null,"abstract":"<p>Chaos intermittency is composed of a laminar regime, which exhibits almost periodic motion, and a burst regime, which exhibits chaotic motion; it is known that in chaos intermittency, switching between these regimes occurs irregularly. In the laminar regime of chaos intermittency, the periodic solution before the saddle node bifurcation is closely related to its generation, and its behavior becomes periodic in a short time; the laminar is not, however, a periodic solution, and there are no unstable periodic solutions nearby. Most chaos control methods cannot be applied to the problem of stabilizing a laminar response to a periodic solution since they refer to information about unstable periodic orbits. In this paper, we demonstrate a control method that can be applied to the control target with laminar phase of a dynamical system exhibiting chaos intermittency. This method records the time series of a periodic solution prior to the saddle node bifurcation as a pseudo-periodic orbit and feeds it back to the control target. We report that when this control method is applied to a circuit model, laminar motion can be stabilized to a periodic solution via control inputs of very small magnitude, for which robust control can be obtained.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154298","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}

{"title":"Slow Invariant Manifolds of Memristor-Based Chaotic Circuits","authors":"Jean-Marc Ginoux, Riccardo Meucci, Guanrong Chen, Leon O. Chua","doi":"10.1142/s0218127424300039","DOIUrl":"https://doi.org/10.1142/s0218127424300039","url":null,"abstract":"<p>This work presents an efficient approach for computing the <i>slow invariant manifold</i> of the fourth-order canonical memristor-based Chua circuits using the <i>flow curvature method</i>. First, the magnetic-flux and charge characteristic curve is generated from the classical circuit with a piecewise-linear function. Then, the characteristic curve is generated from the circuit with the piecewise-linear function replaced by a cubic function. Further, the <i>duality principle</i> is applied to studying such memristor-based circuits in the three-dimensional flux-linkage and charge phase space and then in the four-dimensional current–voltage phase space. It is demonstrated that the slow invariant manifolds of these fourth-order memristor-based chaotic circuits can be more directly computed for the first case than the second.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154750","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}

{"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":"<p>In our earlier research (see [Katsanikas &amp; 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 &amp; 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.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"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}