IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0253830

Haifang Song, Bo Ren

{"title":"General rogue waves and modulation instability of the generalized coupled nonlinear Schrödinger system in optical pulses.","authors":"Haifang Song, Bo Ren","doi":"10.1063/5.0253830","DOIUrl":"https://doi.org/10.1063/5.0253830","url":null,"abstract":"We focus on rogue waves and modulation instability (MI) of the generalized coupled nonlinear Schrödinger (GCNLS) system in optical pulses. Through the Kadomtsev-Petviashvili hierarchy reduction method, general high-order rogue wave solutions in Gram determinant form at p=p0 are constructed, which contain derivative operators with respect to parameters p and q. We reduce solutions to purely algebraic expressions with the aid of the elementary Schur polynomials. The multiplicity of p0 determines the structures of rogue waves and generates diverse patterns. The structures of Nth-order rogue waves are composed of N(N+1)/2 fundamental ones while p0 is a simple root. Free parameters aj play an important part in the patterns of Nth-order rogue waves, large values of a3 lead to triangle structures while large values of a5 yield pentagonal shapes. When p0 is a double root, rogue waves are given by 2×2 block determinants. They are degenerate solutions with N1=0 or N2=0, and they are non-degenerate solutions under the constraint N1,N2>0. Dynamics of degenerate and non-degenerate rogue waves exhibit significant difference from the former case. MI of the GCNLS system is investigated by linear stability analysis since it is closely associated with the excitation of rogue waves. Effects of different parameters on distributions of the growth rate G for MI are considered. Numerical results suggest that amplitudes Aj and wave numbers kj(j=1,2) of the background fields control the widths and positions of MI areas. The results can help us better understand some specific physical issues, especially the propagation in optical fibers.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143572174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analytical treatment of a non-integrable pendulum based on eigenvalue problem of the Liouville operator. 基于Liouville算子特征值问题的不可积摆的解析处理。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0236127

Kosuke Asano, Kenichi Noba, Tomio Petrosky

{"title":"Analytical treatment of a non-integrable pendulum based on eigenvalue problem of the Liouville operator.","authors":"Kosuke Asano, Kenichi Noba, Tomio Petrosky","doi":"10.1063/5.0236127","DOIUrl":"https://doi.org/10.1063/5.0236127","url":null,"abstract":"We perform analytical and quantitative analyses of the motion of a non-integrable pendulum with two degrees of freedom, in which an integrable nonlinear pendulum and a harmonic oscillator are weakly coupled through a non-integrable perturbative interaction, based on the eigenvalue problem of the Liouvillian, which is the generator of time evolution in classical mechanics. The eigenfunctions belonging to the zero eigenvalue of the Liouvillian correspond to the invariants of the motion. The zero eigenvalue of the integrable unperturbed Liouvillian is infinitely degenerate at the resonance point. By applying a perturbation, level repulsion occurs between the eigenstates of the unperturbed system, and some of the degeneracy is lifted, resulting in a non-zero eigenvalue. In order to evaluate the frequency gap caused by the level repulsion, we introduce an auxiliary operator called the collision operator, which is well known in non-equilibrium statistical mechanics. We show that the dependence of the magnitude of a frequency gap on the coupling constant can be quantitatively evaluated by simply finding the condition for the existence of the collision operator, without directly solving the eigenvalue problem.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143603845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Unveiling the dynamics of multi-peak gap nematicons: Effects of thermal response and diffractive radiation. 揭示多峰间隙向列阵的动力学：热响应和衍射辐射的影响。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0250198

Sajitha N M, Suneera T P

引用次数: 0

Strong and weak prediction of stochastic dynamics using reservoir computing. 利用储层计算进行随机动力学的强弱预测。

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0252908

Alexander E Hramov, Nikita Kulagin, Alexander N Pisarchik, Andrey V Andreev

{"title":"Strong and weak prediction of stochastic dynamics using reservoir computing.","authors":"Alexander E Hramov, Nikita Kulagin, Alexander N Pisarchik, Andrey V Andreev","doi":"10.1063/5.0252908","DOIUrl":"https://doi.org/10.1063/5.0252908","url":null,"abstract":"We propose an approach to replicate a stochastic system and forecast its dynamics using a reservoir computing (RC). We show that such machine learning models enable the prediction of the behavior of stochastic systems in a wide range of control parameters. However, the quality of forecasting depends significantly on the training approach used for the RC. Specifically, we distinguish two types of prediction-weak and strong predictions. We get what is called a strong prediction when the testing parameters are close to the training parameters, and almost a true replica of the system trajectory is obtained, which is determined by noise and initial conditions. On the contrary, we call the prediction weak if we can only predict probabilistic characteristics of a stochastic process, which happens if there exists a mismatch between training and testing parameters. The efficiency of our approach is demonstrated with the models of single and coupled stochastic FitzHugh-Nagumo oscillators and the model of an erbium-doped fiber laser with noisy diode pumping. With the help of a RC, we predict the system dynamics for a wide range of noise parameters. In addition, we find a particular regime when the model exhibits switches between strong and weak prediction types, resembling probabilistic properties of on-off intermittency.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143662278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mechanisms for bump state localization in two-dimensional networks of leaky integrate-and-fire neurons. 二维漏整合-发射神经元网络中凹凸状态定位的机制

IF 2.7 2区数学

Chaos Pub Date : 2025-03-01 DOI: 10.1063/5.0244833

A Provata, J Hizanidis, K Anesiadis, O E Omel'chenko

{"title":"Mechanisms for bump state localization in two-dimensional networks of leaky integrate-and-fire neurons.","authors":"A Provata, J Hizanidis, K Anesiadis, O E Omel'chenko","doi":"10.1063/5.0244833","DOIUrl":"https://doi.org/10.1063/5.0244833","url":null,"abstract":"Networks of nonlocally coupled leaky integrate-and-fire neurons exhibit a variety of complex collective behaviors, such as partial synchronization, frequency or amplitude chimeras, solitary states, and bump states. In particular, the bump states consist of one or many regions of asynchronous elements within a sea of subthreshold (quiescent) elements. The asynchronous domains travel in the network in a direction predetermined by the initial conditions. In the present study, we investigate the occurrence of bump states in networks of leaky integrate-and-fire neurons in two-dimensions using nonlocal toroidal connectivity, and we explore possible mechanisms for stabilizing the moving asynchronous domains. Our findings indicate that (I) incorporating a refractory period can effectively anchor the position of these domains in the network, and (II) the switching off of some randomly preselected nodes (i.e., making them permanently idle/inactive) can likewise contribute to stabilizing the positions of the asynchronous domains. In particular, in case II for large values of the coupling strength and a large percentage of idle elements, all nodes acquire different fixed (frozen) values in the quiescent region and oscillations cease throughout the network due to self-organization. For the special case of stationary bump states, we propose an analytical approach to predict their properties. This approach is based on the self-consistency argument and is valid for infinitely large networks. Case I is of particular biomedical interest in view of the importance of refractoriness for biological neurons, while case II can be biomedically relevant when designing therapeutic methods for stabilizing moving signals in the brain.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 3","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143669287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamic incentives and environmental feedback in public goods games: Promoting cooperation through critical thresholds. 公共产品博弈中的动态激励与环境反馈：通过临界阈值促进合作。

IF 2.7 2区数学

Chaos Pub Date : 2025-02-01 DOI: 10.1063/5.0235953

Die Hu, Jinzhuo Liu, Chen Liu, Chen Chu

{"title":"Dynamic incentives and environmental feedback in public goods games: Promoting cooperation through critical thresholds.","authors":"Die Hu, Jinzhuo Liu, Chen Liu, Chen Chu","doi":"10.1063/5.0235953","DOIUrl":"https://doi.org/10.1063/5.0235953","url":null,"abstract":"Understanding the emergence and maintenance of cooperation in multiplayer games is a significant challenge across various theoretical disciplines. In this paper, we introduce an innovative model to study the impacts of environmental feedback in systems with critical thresholds. Different from prior studies on public goods games with environmental feedback, we propose that the system holds expectations for collective behavior, and the dynamic incentives are equal for all group members. Our findings reveal that dynamic incentives driven by environmental feedback significantly enhance cooperation, particularly in scenarios with low synergy factors. As incentives increase, the system shifts from the non-cooperative to cooperative state. Moreover, a faster rate of incentive growth leads to a higher level of cooperation, demonstrating a strong positive correlation between dynamic incentive levels and overall cooperation within the system. Counterintuitively, our study finds that introducing dynamic incentives from environmental feedback not only effectively promotes cooperation under high expectation levels but also surprisingly increases the success rate of cooperation as expectations rise.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143122338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Evolutionary multi-agent reinforcement learning in group social dilemmas. 群体社会困境中的进化多代理强化学习。

IF 2.7 2区数学

Chaos Pub Date : 2025-02-01 DOI: 10.1063/5.0246332

B Mintz, F Fu

{"title":"Evolutionary multi-agent reinforcement learning in group social dilemmas.","authors":"B Mintz, F Fu","doi":"10.1063/5.0246332","DOIUrl":"https://doi.org/10.1063/5.0246332","url":null,"abstract":"Reinforcement learning (RL) is a powerful machine learning technique that has been successfully applied to a wide variety of problems. However, it can be unpredictable and produce suboptimal results in complicated learning environments. This is especially true when multiple agents learn simultaneously, which creates a complex system that is often analytically intractable. Our work considers the fundamental framework of Q-learning in public goods games, where RL individuals must work together to achieve a common goal. This setting allows us to study the tragedy of the commons and free-rider effects in artificial intelligence cooperation, an emerging field with potential to resolve challenging obstacles to the wider application of artificial intelligence. While this social dilemma has been mainly investigated through traditional and evolutionary game theory, our work connects these two approaches by studying agents with an intermediate level of intelligence. We consider the influence of learning parameters on cooperation levels in simulations and a limiting system of differential equations, as well as the effect of evolutionary pressures on exploration rate in both of these models. We find selection for higher and lower levels of exploration, as well as attracting values, and a condition that separates these in a restricted class of games. Our work enhances the theoretical understanding of recent techniques that combine evolutionary algorithms with Q-learning and extends our knowledge of the evolution of machine behavior in social dilemmas.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143398313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exploring the role of synaptic plasticity in the frequency-dependent complexity domain. 探索突触可塑性在频率相关复杂性领域中的作用。

IF 2.7 2区数学

Chaos Pub Date : 2025-02-01 DOI: 10.1063/5.0239820

Monserrat Pallares Di Nunzio, Juan Martín Tenti, Marcelo Arlego, Osvaldo A Rosso, Fernando Montani

{"title":"Exploring the role of synaptic plasticity in the frequency-dependent complexity domain.","authors":"Monserrat Pallares Di Nunzio, Juan Martín Tenti, Marcelo Arlego, Osvaldo A Rosso, Fernando Montani","doi":"10.1063/5.0239820","DOIUrl":"https://doi.org/10.1063/5.0239820","url":null,"abstract":"The involvement of the neocortex in memory processes depends on neuronal plasticity, the ability to restructure inter-neuronal connections, which is essential for learning and long-term memory. Understanding these mechanisms is crucial for advancing early diagnosis and treatment of cognitive disorders such as Parkinson's, epilepsy, and Alzheimer's disease. This study explores a neuronal model with expanded populations, using information-theoretic cues to uncover dynamics underlying plasticity. By employing Bandt-Pompe's entropy-complexity (H×C) and Fisher entropy-information (H×F) planes, hidden patterns in neuronal activity are revealed. These methodologies are particularly suitable for analyzing nonlinear dynamics and causal relationships in time series. In addition, the Hénon map is applied to capture nonlinear behaviors, such as neural firing, highlighting the trade-off between stability and unpredictability in neural networks. Our approach integrates local field potential and intracranial electroencephalograms' data in multiple frequency bands, connecting computational models with experimental evidence. By addressing higher-order interactions, such as action potential triplets, this work advances the understanding of synaptic adjustments and their implications for neuronal complexity and cognitive disorders.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143398315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Stability and Hopf bifurcation analysis of a predator-prey system with multiple delays and generalized Allee effect. 一类具有广义Allee效应的多时滞捕食系统的稳定性和Hopf分岔分析。

IF 2.7 2区数学

Chaos Pub Date : 2025-02-01 DOI: 10.1063/5.0233571

Gaji Zhuo, Hua Liu, Chunya Liu, Qibin Zhang, Yumei Wei

{"title":"Stability and Hopf bifurcation analysis of a predator-prey system with multiple delays and generalized Allee effect.","authors":"Gaji Zhuo, Hua Liu, Chunya Liu, Qibin Zhang, Yumei Wei","doi":"10.1063/5.0233571","DOIUrl":"https://doi.org/10.1063/5.0233571","url":null,"abstract":"In this paper, we develop a predator-prey system with a parameterized generalized Allee effect function and multiple discrete delays. One delay accounts for the negative feedback in the prey, while the other represents the gestation period in the predator population. First, we demonstrate the positivity and boundedness of solutions for the non-delayed system and establish conditions for the existence and stability of equilibria. For the delayed model, we assess the impact of varying delays on the stability of equilibria, discovering that the system exhibits Hopf bifurcations for both delays. Additionally, we determine the crossing curves to explore the stability transitions of equilibria within the delay parameter space. By computing the normal form, we determine the direction, stability, and period of bifurcating periodic solutions. Finally, numerical simulations are conducted to validate the theoretical findings. These simulations reveal that for the Allee effect function considered in this paper, the stability of the system remains unaffected when the delay is comparatively minor. Nonetheless, as the delay grows, the system shifts from a state of stability to one of instability, which even leads to chaotic dynamics. Additionally, the combination of the two delays makes the oscillation frequency of the original chaos higher.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143439932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reservoir computing approaches to unsupervised concept drift detection in dynamical systems. 动态系统中无监督概念漂移检测的油藏计算方法。

IF 2.7 2区数学

Chaos Pub Date : 2025-02-01 DOI: 10.1063/5.0234779

Braden J Thorne, Débora C Corrêa, Ayham Zaitouny, Michael Small, Thomas Jüngling

{"title":"Reservoir computing approaches to unsupervised concept drift detection in dynamical systems.","authors":"Braden J Thorne, Débora C Corrêa, Ayham Zaitouny, Michael Small, Thomas Jüngling","doi":"10.1063/5.0234779","DOIUrl":"https://doi.org/10.1063/5.0234779","url":null,"abstract":"While the assumption that dynamical systems are stationary is common for modeling purposes, in reality, this is rarely the case. Rather, these systems can change over time, a phenomenon referred to as concept drift in the modeling community. While there exist numerous statistics-based methods for concept drift detection on stochastic processes, approaches leveraging nonlinear time series analysis (NTSA) are rarer but seeing increased focus in cases where the processes are deterministic. In this work, we propose a novel approach to unsupervised concept drift detection in dynamical systems utilizing the embedding offered by a reservoir computing (RC) model. This approach is inspired by the performance of RC on supervised classification tasks that indicates a strong ability to characterize dynamical systems. We assess this method on a number of synthetic drifting data streams from dynamical systems as well as an experimental case concerning faulty ball bearing. Our results suggest that the RC based methods are able to generally outperform the existing NTSA methods across the test cases. We conclude our work with some comments regarding real-time implementation and the impact of hyper-parameters on the proposed algorithm.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 2","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143390346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Chaos最新文献