IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0223870

Xueping Cheng, Guiming Jin, Jianan Wang

{"title":"Multiple Lax integrable higher dimensional AKNS(-1) equations and sine-Gordon equations.","authors":"Xueping Cheng, Guiming Jin, Jianan Wang","doi":"10.1063/5.0223870","DOIUrl":"https://doi.org/10.1063/5.0223870","url":null,"abstract":"Through the modified deformation algorithm related to conservation laws, the (1+1)-dimensional AKNS(-1) equations are extended to a (4+1)-dimensional AKNS(-1) system. When one, two, or three of the independent variables are removed, the (4+1)-dimensional AKNS(-1) system degenerates to some novel (3+1)-dimensional, (2+1)-dimensional, and (1+1)-dimensional AKNS(-1) systems, respectively. Under a simple dependent transformation, the (1+1)-dimensional AKNS(-1) equations turn into the classical sine-Gordon equation. Then using the same deformation procedure, the (1+1)-dimensional sine-Gordon equation is generalized to a (3+1)-dimensional version. By introducing the deformation operators to the Lax pairs of the original (1+1)-dimensional models, the Lax integrability of both the (4+1)-dimensional AKNS(-1) system and the (3+1)-dimensional sine-Gordon equation is proven. Finally, the traveling wave solutions of the (4+1)-dimensional AKNS(-1) system and the (3+1)-dimensional sine-Gordon equation are implicitly given and expressed by tanh function and incomplete elliptic integral, respectively. These results may enhance our understanding of the complex physical phenomena described by the nonlinear system discussed in this paper.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142342593","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

Wave breaking, dispersive shock wave, and phase shift for the defocusing complex modified KdV equation. 离焦复变修正 KdV 方程的破波、色散冲击波和相移。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0231741

Ya-Hui Huang, Rui Guo

引用次数: 0

Growing simplicial complex with face dimension selection and preferential attachment. 用面维度选择和优先附着法生长简并复合体

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0210960

Mengjun Ding, Jia Yu, Weiqiang Sun

引用次数: 0

On the timescales in the chaotic dynamics of a 4D symplectic map. 论四维交点图混沌动力学的时间尺度。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0232321

Pablo M Cincotta, Claudia M Giordano

{"title":"On the timescales in the chaotic dynamics of a 4D symplectic map.","authors":"Pablo M Cincotta, Claudia M Giordano","doi":"10.1063/5.0232321","DOIUrl":"https://doi.org/10.1063/5.0232321","url":null,"abstract":"In this work, we investigate different timescales of chaotic dynamics in a multi-parametric 4D symplectic map. We compute the Lyapunov time and a macroscopic timescale, the instability time, for a wide range of values of the system's parameters and many different ensembles of initial conditions in resonant domains. The instability time is obtained by plain numerical simulations and by its estimates from the diffusion time, which we derive in three different ways: through a normal and an anomalous diffusion law and by the Shannon entropy, whose formulation is briefly revisited. A discussion about which of the four approaches provide reliable values of the timescale for a macroscopic instability is addressed. The relationship between the Lyapunov time and the instability time is revisited and studied for this particular system where in some cases, an exponential or polynomial law has been observed. The main conclusion of the present research is that only when the dynamical system behaves as a nearly ergodic one such relationship arises and the Lyapunov and instability times are global timescales, independent of the position in phase space. When stability regions prevent the free diffusion, no correlations between both timescales are observed, they are local and depend on both the position in phase space and the perturbation strength. In any case, the instability time largely exceeds the Lyapunov time. Thus, when the system is far from nearly ergodic, the timescale for predictable dynamics is given by the instability time, being the Lyapunov time its lower bound.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142371126","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

Catalytic evolution of cooperation in a population with behavioral bimodality. 行为双模性群体中合作的催化进化

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0231772

Anhui Sheng, Jing Zhang, Guozhong Zheng, Jiqiang Zhang, Weiran Cai, Li Chen

{"title":"Catalytic evolution of cooperation in a population with behavioral bimodality.","authors":"Anhui Sheng, Jing Zhang, Guozhong Zheng, Jiqiang Zhang, Weiran Cai, Li Chen","doi":"10.1063/5.0231772","DOIUrl":"https://doi.org/10.1063/5.0231772","url":null,"abstract":"The remarkable adaptability of humans in response to complex environments is often demonstrated by the context-dependent adoption of different behavioral modes. However, the existing game-theoretic studies mostly focus on the single-mode assumption, and the impact of this behavioral multimodality on the evolution of cooperation remains largely unknown. Here, we study how cooperation evolves in a population with two behavioral modes. Specifically, we incorporate Q-learning and Tit-for-Tat (TFT) rules into our toy model and investigate the impact of the mode mixture on the evolution of cooperation. While players in a Q-learning mode aim to maximize their accumulated payoffs, players within a TFT mode repeat what their neighbors have done to them. In a structured mixing implementation where the updating rule is fixed for each individual, we find that the mode mixture greatly promotes the overall cooperation prevalence. The promotion is even more significant in the probabilistic mixing, where players randomly select one of the two rules at each step. Finally, this promotion is robust when players adaptively choose the two modes by a real-time comparison. In all three scenarios, players within the Q-learning mode act as catalyzers that turn the TFT players to be more cooperative and as a result drive the whole population to be highly cooperative. The analysis of Q-tables explains the underlying mechanism of cooperation promotion, which captures the \"psychological evolution\" in the players' minds. Our study indicates that the variety of behavioral modes is non-negligible and could be crucial to clarify the emergence of cooperation in the real world.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142388455","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

On coupled oscillators modeling bio-inspired acoustic sensors: Bifurcation analysis toward tunability enhancement. 生物启发声学传感器建模耦合振荡器：面向可调性增强的分岔分析

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0217847

H F J Rolf, T Meurer

{"title":"On coupled oscillators modeling bio-inspired acoustic sensors: Bifurcation analysis toward tunability enhancement.","authors":"H F J Rolf, T Meurer","doi":"10.1063/5.0217847","DOIUrl":"https://doi.org/10.1063/5.0217847","url":null,"abstract":"Oscillators exhibiting an Andronov-Hopf bifurcation are candidates to mimic the functionality of the cochlea, since the transfer response of these oscillators is compressive and frequency selective. The former implies that small stimuli are amplified and strong stimuli are attenuated, while the latter means that the oscillator only reacts in a (small) frequency band. However, this implies that many oscillators are needed to cover a relevant frequency band. By introducing the notion of tunable characteristic frequencies, i.e., the characteristic frequency can be adjusted by a controllable input, the number of oscillators can be eventually reduced. Subsequently, the tunability enhancement of coupled oscillators is investigated by analyzing the local dynamics of a network of oscillators. For this, necessary conditions for the emergence of Andronov-Hopf bifurcations are determined for networks consisting of two groups, i.e., a group is a network of identical oscillators. By choosing the eigenvalues of the product of the cross-coupling matrix as bifurcation parameters and exploiting the structure of the transfer matrix of this network, the critical points and, thus, the characteristic frequency at this point can be derived. Tunability of the characteristic frequency is then enabled by controlling the asymmetry between the groups of oscillators.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142459303","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

Threshold incentive mechanisms for the sustainable management of public resources. 公共资源可持续管理的门槛激励机制。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0233220

Lichen Wang, Shijia Hua, Yuyuan Liu, Liang Zhang, Linjie Liu

{"title":"Threshold incentive mechanisms for the sustainable management of public resources.","authors":"Lichen Wang, Shijia Hua, Yuyuan Liu, Liang Zhang, Linjie Liu","doi":"10.1063/5.0233220","DOIUrl":"https://doi.org/10.1063/5.0233220","url":null,"abstract":"Maintaining global ecological balance is inextricably linked to the effective governance of public resources. Previous studies have proposed the introduction of incentive mechanisms to mitigate the defection behavior within the scope of public resource management to facilitate sustainable utilization. However, these incentive strategies often present a considerable financial burden. Here, we first propose a two-threshold incentive scheme based on group state objectives, where the reward mechanism is triggered when the number of cooperators is below the threshold M, and the punishment mechanism is triggered when the number of cooperators is above the threshold Q. We further introduce an incentive mechanism by considering both resource and group thresholds, where incentives are implemented separately when the number of cooperators and the current quantity of resources meet thresholds. Our theoretical results reveal that introducing these two new mechanisms can effectively maintain cooperative behavior and sustainable resources while reducing management costs. However, if the initial resource level is low, the tragedy of the commons will still occur. It is recommended that the number of developers be reduced, the allocation be lowered, or the development simply suspended and the natural regeneration of resources be waited for.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142521136","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

Thoughtful data analysis. 深思熟虑的数据分析。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0230739

Elizabeth Bradley, James W C White, Joshua Garland

引用次数: 0

When multi-group selection meets mystery of cooperation in structured public goods games. 当多群体选择与结构化公共产品博弈中的合作奥秘相遇时。

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0234041

Xinyu Liu, Baosen Yang, Zhao-Long Hu, Mohammed A A Al-Qaness, Changbing Tang

{"title":"When multi-group selection meets mystery of cooperation in structured public goods games.","authors":"Xinyu Liu, Baosen Yang, Zhao-Long Hu, Mohammed A A Al-Qaness, Changbing Tang","doi":"10.1063/5.0234041","DOIUrl":"https://doi.org/10.1063/5.0234041","url":null,"abstract":"Cooperation is the cornerstone of social stability and human development. In order to promote mutual cooperation among individuals, some researchers analyzed the important factors influencing individual behavior from the perspective of group selection, while others revealed the evolutionary mechanism of cooperative behavior in groups from the perspective of network reciprocity. However, group selection and network reciprocity actually work together and simultaneously drive individuals to cooperate with each other. Analyzing each mechanism in isolation provides an incomplete understanding of the interaction process. Inspired by this, we integrate the coupled effects of both group selection and network reciprocity on the behavior of individuals. We develop a structured public goods game model to study the evolution of individual cooperative behavior in multiple groups, where each individual can interact not only with intra-group individuals but also with inter-group individuals. Based on the fixed probabilities of multi-group selection, including intra-group and inter-group selection, we derive a general condition that promotes cooperation among individuals. Besides, we discuss the effects of the number of neighbors in a group, group size, and group size on the selection of cooperative behavior. Finally, we systematically compare our model with the well-mixed case, and the results show that a structured population enhances cooperation. Increasing the number of populations boosts the fixation probability of cooperation. To the best of our knowledge, this paper is the first to study the cooperative evolutionary dynamics of multi-group selection in structured populations through public goods games.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142496090","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

Butterflies and bifurcations in surface radio-frequency traps: The diversity of routes to chaos. 表面射频陷阱中的蝴蝶和分岔：通往混沌之路的多样性

IF 2.7 2区数学

Chaos Pub Date : 2024-10-01 DOI: 10.1063/5.0223552

S Rudyi, D Shcherbinin, A Ivanov

引用次数: 0

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