International Journal of Bifurcation and Chaos最新文献

{"title":"An Integrated Reservoir Predictor Based on Spatiotemporal Information Transformation","authors":"Na Yang, Renhao Hong, Pei Chen, Zhengrong liu","doi":"10.1142/s0218127424500482","DOIUrl":"https://doi.org/10.1142/s0218127424500482","url":null,"abstract":"<p>Multistep prediction of high-dimensional time series is an essential and challenging task. In this study, we propose an integrated reservoir predictor for making accurate and robust multistep-ahead forecasts based on short-term high-dimensional time series. Initially, a conjugated pair of Spatiotemporal Information (STI) equations is derived using Takens’ embedding theory to transform the spatial information of high-dimensional variables into one-dimensional temporal information of the target variable and vice versa. Next, by exploiting reservoir networks, reservoir-based STI equations are established to efficiently capture nonlinear dynamics of the target system with only linear optimization. Then, through an integration phase, the integrated reservoir predictor can output precise and robust predictions of the multistep-ahead states of any target variable. The integrated reservoir predictor outperforms some other prediction methods (including reservoir computing, long-short-term-memory network, convolutional neural network and support vector regression), when applied to classical dynamic systems (e.g. 60D double scroll model, 40D Lorenz 96 model, and 60D Rössler model) and real-world datasets (solar generation data and PM2.5 concentration records), as indicated by evaluation metrics such as Pearson correlation coefficients exceeding 0.9 and root-mean-square errors below 0.3, even in the presence of noise in training data.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140577468","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":"Designing a Fully Current-Controlled Memristors-Based Oscillator","authors":"Yan Liang, Shichang Wang, Zhenzhou Lu, Yiqing Li, Kangtai Wang","doi":"10.1142/s0218127424500421","DOIUrl":"https://doi.org/10.1142/s0218127424500421","url":null,"abstract":"<p>One of the promising applications of locally-active memristors (LAMs) is to construct oscillators for oscillatory neural networks. By using two current-controlled (CC) LAMs, a fully CC LAM-based oscillator is designed in this paper. The oscillator principle originates from the small-signal inductive and capacitive impedance characteristics of two different CC LAMs, and thus extra reactance element is not required in the circuit. Based on bifurcation theory and small-signal analysis method, conditions of the equilibrium point instability are quantitatively derived. Theoretical analysis indicates that the circuit oscillation is dependent on three critical parameters. Then, according to the conditions of the equilibrium point instability, parameters design methods of the two LAMs are proposed, including the static and dynamic parameters. A simple NbO_<i>x</i> CC LAM model is taken as an example to conduct detailed simulation analysis. The simulation results verify the feasibility of the proposed circuit and analysis methods. Finally, the effects of the LAM model parameters on the oscillator performance are investigated, which is helpful for optimal design of the oscillator.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140588360","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":"Influence of Two-Frequency Rotational Modulation on the Dynamics of the Rayleigh–Bénard Convection in Water-Based Nanoliquids with Either AA7072 or AA7075 Nanoparticles","authors":"C. Kanchana, P. G. Siddheshwar, D. Laroze","doi":"10.1142/s0218127424500433","DOIUrl":"https://doi.org/10.1142/s0218127424500433","url":null,"abstract":"<p>The effect of time-periodic two-frequency rotation modulation on Rayleigh–Bénard convection in water with either AA7072 or AA7075 nanoparticles is investigated. The single-phase description of the Khanafer–Vafai–Lightstone model is used for modeling the nanoliquids. An asymptotic expansion procedure is adopted in the case of the linear stability to obtain the correction (due to modulation) to the Rayleigh number at marginal stability of unmodulated convection. A nonlinear regime of convection is considered with a nonautonomous generalized Lorenz model as the governing equation. The method of multiscales is then employed to obtain the coupled nonautonomous Ginzburg–Landau equations with cubic nonlinearity from the Lorenz model. These equations are presented in the phase-amplitude form and the amplitude is used to quantify the heat transport. The modulation amplitude is considered to be small (of order less than unity) and moderate frequencies of modulation are considered. We found that there is a threshold frequency beyond which the system behavior reverses. At frequencies below the threshold, the mean Nusselt number increases with an increase in the amplitude of modulation while an opposite influence is seen for values above the threshold. Such a behavior is a consequence of what is analogously seen in the case of the critical Rayleigh number. The influence of two-frequency modulation is more pronounced on the results of the linear and nonlinear regimes compared to that of the single-frequency one. The heat transport is enhanced due to the presence of dilute concentration of suspended nanoparticles (either AA7072 or AA7075 nanoalloys) in water. The influence of nanoparticles is to modify the threshold values generating chaos but it does not qualitatively alter the dynamical behavior of the system. The plots of Lyapunov exponents reveal that there is no possibility of hyper-chaos in the generalized Lorenz model when there is a rotational modulation.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323309","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 Predator-Driven Allee and Spatiotemporal Effect on a Simple Predator–Prey Model","authors":"Kaushik Kayal, Sudip Samanta, Sourav Rana, Sagar Karmakar, Joydev Chattopadhyay","doi":"10.1142/s0218127424500469","DOIUrl":"https://doi.org/10.1142/s0218127424500469","url":null,"abstract":"<p>In this research paper, we consider a Leslie–Gower Reaction–Diffusion (RD) model with a predator-driven Allee term in the prey population. We derive conditions for the existence of nontrivial solutions, uniform boundedness, local stability at co-existing equilibrium points, and Hopf bifurcation criteria from the temporal system. We identify sufficient conditions for Turing instability with no-flux boundary condition for the spatial system. Our investigation delves into the analysis of diffusion-induced Turing instability, incorporating stability conditions for the constant steady-state in the spatial model. We also investigate the conditions for the existence and nonexistence of nonconstant steady states in the diffusion-induced model. During numerical simulations, we observe that the predator-driven Allee term is essential for the model to generate Turing structures. Our findings reveal intriguing properties within the RD system, demonstrating its ability to produce patterns within the Turing domain. The simulation confirms that cold–hot spots and stripes-like patterns (a mixture of spots and strips) arises for different strengths of the predation parameter and Allee parameter. In contrast, we observe that for the above threshold value of the Allee parameter, the above-mentioned patterns may disappear from the system. Interestingly, we also observe that the stationary system produces patterns for both large and small amplitudes of perturbation in the vicinity of the Turing boundary. Our research may contribute valuable insights into the Allee effect and enhance our understanding of predator–prey interactions in naturalistic environments.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323501","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":"Bifurcations for Homoclinic Networks in Two-Dimensional Polynomial Systems","authors":"Albert C. J. Luo","doi":"10.1142/s0218127424300064","DOIUrl":"https://doi.org/10.1142/s0218127424300064","url":null,"abstract":"<p>The bifurcation theory for homoclinic networks with singular and nonsingular equilibriums is a key to understand the global dynamics of nonlinear dynamical systems, which will help one determine the dynamical behaviors of physical and engineering nonlinear systems. In this paper, the appearing and switching bifurcations for homoclinic networks through equilibriums in planar polynomial dynamical systems are studied. The appearing and switching bifurcations are discussed for the homoclinic networks of nonsingular and singular sources, sinks, saddles with singular saddle-sources, saddle-sinks, and double-saddles in self-univariate polynomial systems. The first integral manifolds for nonsingular and singular equilibrium networks are determined. The illustrations of singular equilibriums to networks of nonsingular sources, sinks and saddles are given. The appearing and switching bifurcations are studied for homoclinic networks of singular and nonsingular saddles and centers with singular parabola-saddles and double-inflection saddles in crossing-univariate polynomial systems, and the first integral manifolds of such homoclinic networks are determined through polynomial functions. The illustrations of singular equilibriums to networks of nonsingular saddles and centers are given. This paper may help one understand higher-order bifurcation theory in nonlinear dynamical systems, which is completely different from the classic bifurcation theories.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140323493","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":"Functional Shift-Induced Degenerate Transcritical Neimark–Sacker Bifurcation in a Discrete Hypercycle","authors":"Ernest Fontich, Antoni Guillamon, Júlia Perona, Josep Sardanyés","doi":"10.1142/s0218127424500457","DOIUrl":"https://doi.org/10.1142/s0218127424500457","url":null,"abstract":"<p>In this paper, we investigate the impact of functional shifts in a time-discrete cross-catalytic system. We use the hypercycle model considering that one of the species shifts from a cooperator to a degrader. At the bifurcation caused by this functional shift, an invariant curve collapses to a point <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>P</mi></math></span><span></span> while, simultaneously, two fixed points collide with <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>P</mi></math></span><span></span> in a transcritical bifurcation. Moreover, all points of a line containing <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>P</mi></math></span><span></span> become fixed points at the bifurcation and only at the bifurcation in a degenerate scenario. We provide a complete analytical description of this degenerate bifurcation. As a result of our study, we prove the existence of the invariant curve arising from the transition to cooperation.</p>","PeriodicalId":50337,"journal":{"name":"International Journal of Bifurcation and Chaos","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140205416","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":"Learning Topological Horseshoe via Deep Neural Networks","authors":"Xiao-Song Yang, Junfeng Cheng","doi":"10.1142/s021812742430009x","DOIUrl":"https://doi.org/10.1142/s021812742430009x","url":null,"abstract":"<p>Deep Neural Networks (DNNs) have been successfully applied to investigations of numerical dynamics of finite-dimensional nonlinear systems such as ODEs instead of finding numerical solutions to ODEs via the traditional Runge–Kutta method and its variants. To show the advantages of DNNs, in this paper, we demonstrate that the DNNs are more efficient in finding topological horseshoes in chaotic dynamical systems.</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":"140202487","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":"A Nonlinear Megastable System with Diamond-Shaped Oscillators","authors":"Atefeh Ahmadi, Sridevi Sriram, Ahmed M. Ali Ali, Karthikeyan Rajagopal, Nikhil Pal, Sajad Jafari","doi":"10.1142/s0218127424500536","DOIUrl":"https://doi.org/10.1142/s0218127424500536","url":null,"abstract":"<p>Benefiting from trigonometric and hyperbolic functions, a nonlinear megastable chaotic system is reported in this paper. Its nonlinear equations without linear terms make the system dynamics much more complex. Its coexisting attractors’ shape is diamond-like; thus, this system is said to have diamond-shaped oscillators. State space and time series plots show the existence of coexisting chaotic attractors. The autonomous version of this system was studied previously. Inspired by the former work and applying a forcing term to this system, its dynamics are studied. All forcing term parameters’ impacts are investigated alongside the initial condition-dependent behaviors to confirm the system’s megastability. The dynamical analysis utilizes one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents, Kaplan–Yorke dimension, and attraction basin. Because of this system’s megastability, the one-dimensional bifurcation diagrams and Kaplan–Yorke dimension are plotted with three distinct initial conditions. Its analog circuit is simulated in the OrCAD environment to confirm the numerical simulations’ correctness.</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":"140205415","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":"Analysis of Successive Doubly Nested Mixed-Mode Oscillations","authors":"Hidetaka Ito, Naohiko Inaba","doi":"10.1142/s0218127424500445","DOIUrl":"https://doi.org/10.1142/s0218127424500445","url":null,"abstract":"<p>In previous works [Inaba &amp; Kousaka, 2020; Inaba &amp; Tsubone, 2020; Inaba <i>et al.</i>, 2023], significant bifurcation structures referred to as nested Mixed-Mode Oscillations (MMOs) were found to be present in forced Bonhoeffer–van der Pol (BVP) oscillators. It is well known that unnested Mixed-Mode Oscillation-Incrementing Bifurcations (MMOIBs) can generate <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mo stretchy=\"false\">[</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy=\"false\">×</mo><mi>m</mi><mo stretchy=\"false\">]</mo></math></span><span></span> oscillations (i.e. <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span> followed by <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span> repeated <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi></math></span><span></span> times) for successive values of <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>m</mi></math></span><span></span>, where <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span> and <span><math altimg=\"eq-00007.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span><span></span> are adjacent fundamental simple MMOs, e.g. <span><math altimg=\"eq-00008.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mi>s</mi></mrow></msup></math></span><span></span> and <span><math altimg=\"eq-00009.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msup><mrow><mn>1</mn></mrow><mrow><mi>s</mi><mo stretchy=\"false\">+</mo><mn>1</mn></mrow></msup></math></span><span></span>, where <span><math altimg=\"eq-00010.gif\" display=\"inline\" overflow=\"scroll\"><mi>s</mi></math></span><span></span> is an integer. Furthermore, it has been confirmed that MMOIBs can generate nested MMOs. Let two adjacent unnested MMOIB-generated MMOs be denoted <span><math altimg=\"eq-00011.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>A</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">(</mo><mo>=</mo><mo stretchy=\"false\">[</mo><msub><mrow><mi>A</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>0</mn></mrow></msub><mo stretchy=\"false\">×</mo><mi>m</mi><mo stretchy=\"false\">]</mo><mo stretchy=\"false\">)</mo></math></span><span></span> and <span><math altimg=\"eq-00012.gif\" display=\"inline\" overflow=\"scroll\"><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy=\"false\">(</mo>","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":"140202300","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":"Bifurcation Regulations Induced by Joint Noise in a Tri-Rhythmic Van Der Pol System","authors":"Jing Yuan, Lijuan Ning, Ze Li","doi":"10.1142/s0218127424500512","DOIUrl":"https://doi.org/10.1142/s0218127424500512","url":null,"abstract":"<p>Tri-rhythmical nature has attracted extensive attention from scholars in describing the dynamical behaviors of self-sustained systems. In this paper, we consider a tri-rhythmic van der Pol system and give a bifurcation analysis of a stochastic tri-rhythmic self-sustained system under joint noise perturbation. Based on an approximate approach, we give the stationary probability density function of amplitudes, and we find that the noise and time-delay feedback, regulating the velocity time-delay feedback strength parameter, may not cause transitions among unimodal, bimodal and trimodal in the tri-rhythmic system. More stochastic bifurcations appear by regulating the time delay in this system. The system, surprisingly, undergoes five times of stochastic bifurcations when the time delay is monotonically increased. It is shown that the time delay is more sensitive to the tri-rhythmic system and a much stronger dependence on the system. From a biological point of view, the reaction rate of biological molecules can be enhanced or diminished by the change of the noise intensity or correlation time of Gaussian colored noise. More surprisingly, an increase in displacement feedback will delay the reaction rate; however, the effect of an increase in velocity feedback on the reaction rate depends on the time delay. A detailed research on the parameter space indicates that time delay and colored noise parameters can effectively control the multirhythmicity of the system. Finally, this paper verifies the effectiveness of the theoretical solution through the numerical results of Monte Carlo simulation of the original system. These results may help to further explore forking bifurcations in real-world applications. This research provides new insight into the understanding of nontrivial effects of joint noise on the tri-rhythmic system.</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":"140205355","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}