{"title":"3D Generating Surfaces in Hamiltonian Systems with Three Degrees of Freedom – II","authors":"Matthaios Katsanikas, Stephen Wiggins","doi":"10.1142/s0218127424300052","DOIUrl":"https://doi.org/10.1142/s0218127424300052","url":null,"abstract":"<p>Our paper is a continuation of a previous work referenced as [Katsanikas & Wiggins, 2024b]. In this new paper, we present a second method for computing three-dimensional generating surfaces in Hamiltonian systems with three degrees of freedom. These 3D generating surfaces are distinct from the Normally Hyperbolic Invariant Manifold (NHIM) and have the unique property of producing dividing surfaces with no-recrossing characteristics, as explained in our previous work [Katsanikas & Wiggins, 2024b]. This second method for computing 3D generating surfaces is valuable, especially in cases where the first method is unable to achieve the desired results. This research aims to provide alternative techniques and solutions for addressing specific challenges in Hamiltonian systems with three degrees of freedom and improving the accuracy and reliability of generating surfaces. This research may find applications in the broader field of dynamical systems and attract the attention of researchers and scholars interested in these areas.</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":"140154363","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}
Kangning An, Lin Du, Honghui Zhang, Zhuan Shen, Xiaojuan Sun
{"title":"Transition and Propagation of Epilepsy in an Improved Epileptor Model Coupled with Astrocyte","authors":"Kangning An, Lin Du, Honghui Zhang, Zhuan Shen, Xiaojuan Sun","doi":"10.1142/s0218127424300076","DOIUrl":"https://doi.org/10.1142/s0218127424300076","url":null,"abstract":"<p>In this paper, a tripartite synapse network is constructed to examine external and internal triggering factors of epilepsy transition and propagation in neurons with the Epileptor-2 model. We first explore the external stimuli in the environment that induce epileptic activities and transition behaviors among Ictal Discharges (IDs) and Interictal Discharges (IIDs) states. The higher the strength and abruptness of the stimuli, the more severe is the occurrence of epilepsy within a reasonable range of parameters. Then for the internal triggering factors, the results of the tripartite synapse network, which is improved by combining the Epileptor-2 model with astrocyte by means of ion exchange and new connections, show that astrocytes can transmit normal physiological activity information and filter out abnormal discharge information of neurons. One of the causes for epileptic seizures is the abnormal release of glial neurotransmitters in astrocytes. The excessive release of glutamate causes the discharge state of neurons to transit from nonepileptic to IIDs, IDs and tonic, while adenosine triphosphate can alleviate epilepsy. Meanwhile, the synapse dysfunction of an astrocyte-free network can also lead to seizures, and the epilepsy propagation ability of a tripartite synapse network becomes weaker than that of an astrocyte-free network. Our research is expected to provide some theoretical basis for the therapeutic approach to curing epilepsy in the intracellular and extracellular contexts.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124776","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":"Dynamic Analysis of a Ratio-Dependent Food Chain Model with Prey-Taxis","authors":"Zhuzhen Liao, Cui Song, Zhi-Cheng Wang","doi":"10.1142/s0218127424500378","DOIUrl":"https://doi.org/10.1142/s0218127424500378","url":null,"abstract":"<p>In this paper, we consider a food chain model with ratio-dependent functional response and prey-taxis. We first investigate the global existence and boundedness of the unique positive classical solutions of the system in a bounded domain with smooth boundary and Neumann boundary conditions. Then, we analyze the local stability of the system and the existence of Hopf bifurcation. In addition, we prove the global asymptotic stability of steady states under some conditions by constructing a Lyapunov functional, and investigate convergence rates. Finally, we present several numerical simulations to illustrate the results.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124771","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":"Stability Analysis and Simulation of a Delayed Dengue Transmission Model with Logistic Growth and Nonlinear Incidence Rate","authors":"Fangkai Guo, Xiaohong Tian","doi":"10.1142/s0218127424500287","DOIUrl":"https://doi.org/10.1142/s0218127424500287","url":null,"abstract":"<p>In this work, a dengue transmission model with logistic growth and time delay <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">(</mo><mi>τ</mi><mo stretchy=\"false\">)</mo></math></span><span></span> is investigated. Through detailed mathematical analysis, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed, the existence of Hopf bifurcation and stability switch is established, and it is proved that the system is permanent if the basic reproduction number is greater than 1. On the basis of Lyapunov functional and LaSalle’s invariance principle, sufficient conditions are derived for the global stability of the endemic equilibrium. The primary theoretical results are simulated numerically. In addition, when <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>τ</mi><mo>=</mo><mn>0</mn></math></span><span></span>, relevant properties of the Hopf bifurcation are analyzed. Finally, sensitivity analysis is given and data fitting is carried out to predict the epidemic development trend of dengue fever in Singapore in 2020.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124769","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":"Four Limit Cycles of Three-Dimensional Discontinuous Piecewise Differential Systems Having a Sphere as Switching Manifold","authors":"Louiza Baymout, Rebiha Benterki","doi":"10.1142/s0218127424500305","DOIUrl":"https://doi.org/10.1142/s0218127424500305","url":null,"abstract":"<p>Because of their applications, the study of piecewise-linear differential systems has become increasingly important in recent years. This type of system already exists to model many different natural phenomena in physics, biology, economics, etc. As is well known, the study of the qualitative theory of piecewise differential systems focuses mainly on limit cycles. Most papers studying the problem of existence and the maximum number of limit cycles of piecewise differential systems have precisely considered planar systems. However, few papers have examined this problem in <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>. In this paper, our main goal is to examine a class of discontinuous piecewise differential systems in <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℝ</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span><span></span>, where we consider the unit sphere as the separation surface that divides the entire space into two regions, each one has a linear vector field analogous to planar center. In general, it is hard to determine an exact upper bound for the number of limit cycles that a class of differential systems can exhibit. We prove that this class of differential systems can have at most four limit cycles. We show that there are examples of such differential systems with exactly 1, 2, 3 and 4 limit cycles.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124792","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":"Existence and Uniqueness of a Canard Cycle with Cyclicity at Most Two in a Singularly Perturbed Leslie–Gower Predator–Prey Model with Prey Harvesting","authors":"Zhenshu Wen, Tianyu Shi","doi":"10.1142/s0218127424500366","DOIUrl":"https://doi.org/10.1142/s0218127424500366","url":null,"abstract":"Yao and Huzak [2022] proved that the cyclicity of canard cycles in a singularly perturbed Leslie–Gower predator–prey model with prey harvesting is at most two in a region of parameters. In this paper, we further show that there exists only one canard cycle with cyclicity at most two under explicit parameters conditions.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140077784","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":"Geometrical and Numerical Analysis of Predator–Prey System Based on the Allee Effect in Predator","authors":"M. K. Gupta, Abha Sahu, C. K. Yadav","doi":"10.1142/s0218127424500330","DOIUrl":"https://doi.org/10.1142/s0218127424500330","url":null,"abstract":"This study explores the complex dynamics of the predator–prey interactions, with a specific emphasis on the influence of the Allee effect on the predator population. We examined the fundamental mathematical characteristics of the model under consideration, such as the positivity of the system and the boundedness of the solutions. We investigated the equilibrium points and analyzed their stability using the Jacobi and Lyapunov methods. A comprehensive examination was carried out on the geometric properties of the dynamical system to compute the five invariants of the KCC theory. In particular, the deviation curvature tensor and its eigenvalues are investigated to demonstrate the behavior of the system stability. We have also obtained the necessary and sufficient conditions for the given set of parameters of the system in order to have the Jacobi stability (instability) near the equilibrium point. To visualize the dynamical behavior of the predator–prey model with the Allee effect in the predator density, numerical simulations were conducted. The investigation encompasses an examination of the system’s behavior from both geometric and numerical standpoints, with the objective of attaining a thorough comprehension using few examples.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140078899","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":"Dynamics of a Class of Prey–Predator Models with Singular Perturbation and Distributed Delay","authors":"Jie Gao, Yue Zhang","doi":"10.1142/s0218127424500317","DOIUrl":"https://doi.org/10.1142/s0218127424500317","url":null,"abstract":"<p>In this paper, two prey–predator models with distributed delays are presented based on the growth and loss rates of the predator, which are much smaller than that of the prey, leading to a singular perturbation problem. It is obtained that Hopf bifurcation can occur, where the coexistence equilibrium becomes unstable leading to a stable limit cycle. Subsequently, considering the perturbation parameter <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mn>0</mn><mo><</mo><mi>𝜀</mi><mo>≪</mo><mn>1</mn></math></span><span></span>, the fact that the solution crossing the transcritical point converges to a stable equilibrium is discussed for the model with Holling type I using the linear chain criterion, center-manifold reduction, the geometric singular perturbation theory and entry–exit function. The existence and uniqueness of relaxation oscillation cycle for the model with Holling type II are obtained. In addition, numerical simulations are provided to verify the analytical results.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140124677","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}
Bin Yang, Tao Chen, Ai Chen, Shukai Duan, Lidan Wang
{"title":"A Lightweight CNN Based on Memristive Stochastic Computing for Electronic Nose","authors":"Bin Yang, Tao Chen, Ai Chen, Shukai Duan, Lidan Wang","doi":"10.1142/s0218127424500275","DOIUrl":"https://doi.org/10.1142/s0218127424500275","url":null,"abstract":"<p>Gas detection plays different roles in different environments. Traditional algorithms implemented on electronic nose for gas detection and recognition have high complexity and cannot resist device drift. In response to the above issues, we propose a convolutional neural network based on memristive Stochastic Computing (SC), which combines the characteristics of small devices and low power consumption of memristor devices, as well as the fast and fault-tolerant random calculation speed. It can effectively utilize hardware advantages, recognizing gases by electronic nose. The experimental results show that for two different gas sensor array datasets, the accuracy of the proposed method can achieve the level of 99%. When using memristive SC for deduction, the accuracy decreases by less than 1%, but in drift data, the accuracy can be improved by about 3%. Finally, the improvement in area, power, and energy compared to inference in GPU (NVIDIA Geforce RTX 3060 Laptop) is 1104X, 48X, and 9X, respectively.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129802","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":"Global Phase Portraits of Piecewise Quadratic Differential Systems with a Pseudo-Center","authors":"Meriem Barkat, R. Benterki, Enrique Ponce","doi":"10.1142/s0218127424500329","DOIUrl":"https://doi.org/10.1142/s0218127424500329","url":null,"abstract":"This paper deals with the global dynamics of planar piecewise smooth differential systems constituted by two different vector fields separated by one straight line that passes through the origin. From a quasi-canonical family of piecewise quadratic differential systems with a pseudo-focus point at the origin, which has six parameters, we investigate the subfamilies where the origin is indeed a pseudo-center. For such subfamilies, we classify its global phase portraits in the Poincaré disk and the associated bifurcation sets.","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140078209","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}