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Impacts of reinforcement learning-driven subsidy policies on evolutionary vaccination dynamics. 强化学习驱动的补贴政策对疫苗接种演化动力学的影响。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0306752
Yunxiang Hou, Yongxin Huang, Yikang Lu, Lei Shi

In voluntary vaccination, adaptive adjustments in government subsidy policies play a crucial role in influencing vaccination levels. The Bush-Mosteller model, a type of reinforcement learning, offers an excellent framework to study the decision-making process of the government. In this work, we study how the government adaptively adjusts to different subsidy policies that affect the vaccination level. Here, we incorporate the per capita treatment cost for infections and the per capita subsidy into a Bush-Mosteller model where the former serves as the payoff and the latter defines the aspiration level, and the gap between the payoff and the aspiration level determines whether the stimulus is positive, resulting in continuation of the current policy, or negative, prompting policy adjustment. Our results reveal that while increasing the total subsidy amount can enhance vaccination levels, reducing the relative vaccination costs fails to increase vaccination levels under a fixed subsidy budget. Provided the total subsidy exactly covers vaccination costs, vaccination levels depend on the dominant strategy: dominance of the partial-offset policy results in a decline, dominance of the free subsidy policy leads to an increase, and the coexistence of both policies maintains the initial level. This study sheds light on the role of adaptive subsidy policies driven by reinforcement learning in shaping vaccination dynamics.

在自愿疫苗接种中,政府补贴政策的适应性调整在影响疫苗接种水平方面起着至关重要的作用。Bush-Mosteller模型是强化学习的一种,为研究政府决策过程提供了一个很好的框架。在这项工作中,我们研究了政府如何适应影响疫苗接种水平的不同补贴政策。在这里,我们将人均感染治疗成本和人均补贴纳入到Bush-Mosteller模型中,前者作为收益,后者定义了期望水平,收益与期望水平之间的差距决定了刺激是积极的,从而导致当前政策的延续,还是消极的,从而促使政策调整。研究结果表明,在一定的补贴预算下,增加补贴总额可以提高疫苗接种水平,但降低相对疫苗接种成本并不能提高疫苗接种水平。在补贴总额完全覆盖疫苗接种成本的情况下,疫苗接种水平取决于优势策略:部分抵消政策占主导地位导致疫苗接种水平下降,免费补贴政策占主导地位导致疫苗接种水平上升,两种政策共存时保持初始水平。这项研究揭示了由强化学习驱动的适应性补贴政策在塑造疫苗接种动态中的作用。
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引用次数: 0
Introduction to focus issue: Intelligent game on networked systems: Optimization, evolution and control. 重点课题导论:网络系统上的智能博弈:优化、演化与控制。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0311028
Lin Wang, Yang Lou, Zhihai Rong, Guanrong Chen

Networked systems-from smart grids and autonomous fleets to social networks-are ubiquitous yet complex, with agents interacting amid topological dependencies and challenges like dynamic environments or malicious attacks. Game theory, control theory, and optimization offer tools to model these systems, but bridging theory with real-world complexity remains a key gap. This Chaos Focus Issue tackles this by exploring intelligent game theory in networked systems, featuring 26 papers across four themes: cooperation promotion, distributed systems, complex structures, and game applications. It links theoretical insights (e.g., cooperative dynamics in structured populations) to practical solutions (e.g., epidemic control, infrastructure protection), advancing resilient, efficient networked system design.

网络系统——从智能电网和自动车队到社交网络——无处不在,但却很复杂,代理在拓扑依赖关系和动态环境或恶意攻击等挑战中相互作用。博弈论、控制理论和优化为这些系统建模提供了工具,但将理论与现实世界的复杂性联系起来仍然是一个关键的差距。本期《混沌焦点》通过探索网络系统中的智能博弈论来解决这一问题,刊载了26篇论文,涉及四个主题:合作促进、分布式系统、复杂结构和游戏应用。它将理论见解(例如,结构化人口中的合作动态)与实际解决方案(例如,流行病控制,基础设施保护)联系起来,推进有弹性,高效的网络系统设计。
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引用次数: 0
Quantum signatures of strange attractors. 奇异吸引子的量子特征。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0304784
Bence Dárdai, Gábor Vattay

In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate the quantum Duffing oscillator, a paradigmatic chaotic system, using the Caldirola-Kanai framework, where dissipation is integrated directly into a time-dependent Hamiltonian. By employing the Husimi distribution to represent the quantum state in phase space, we present the first visualization of a quantum strange attractor within this model. Our simulations demonstrate how an initially simple Gaussian wave packet is stretched, folded, and sculpted by the interplay of chaotic dynamics and energy loss, causing it to localize onto a structure that beautifully mirrors the classical attractor. This quantum "photograph" is inherently smoothed, blurring the infinitely fine fractal details of its classical counterpart as a direct consequence of the uncertainty principle. We supplement this analysis by examining the out-of-time-ordered correlator, which shows that stronger dissipation clarifies the exponential growth associated with the classical Lyapunov exponent, thereby confirming the model's semiclassical behavior. This work offers a compelling geometric perspective on open chaotic quantum systems and sheds new light on the quantum-classical transition.

在经典力学中,耗散驱动系统通常表现出复杂的分形动力学,称为奇异吸引子。本文解决了这样的结构如何在量子领域显现的基本问题。我们使用Caldirola-Kanai框架研究了量子Duffing振子,这是一个范式混沌系统,其中耗散直接集成到随时间变化的哈密顿量中。通过采用Husimi分布来表示相空间中的量子态,我们首次在该模型中可视化了量子奇异吸引子。我们的模拟演示了一个最初简单的高斯波包是如何在混沌动力学和能量损失的相互作用下被拉伸、折叠和雕刻的,导致它定位到一个漂亮地反映经典吸引子的结构上。这种量子“照片”本质上是平滑的,模糊了其经典对应物的无限精细的分形细节,这是不确定性原理的直接结果。我们通过检查非时序相关器来补充这一分析,结果表明更强的耗散澄清了与经典Lyapunov指数相关的指数增长,从而证实了模型的半经典行为。这项工作为开放混沌量子系统提供了一个引人注目的几何视角,并为量子-经典跃迁提供了新的视角。
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引用次数: 0
Dispersion-managed electromagnetic pulse transparency in arrays of coupled microcavities. 耦合微腔阵列中色散管理的电磁脉冲透明度。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0295729
Z Ivić, Ž Pržulj, D Chevizovich, G P Tsironis

We examine theoretically the transparency of electromagnetic pulses through an infinite one-dimensional array of coupled optical microcavities uniformly filled with superconducting qubits-one per cavity. Two types of hybrid matter-light waves, i.e., polaritons and self-induced transparency solitons, govern the transparency of electromagnetic radiation in these media. The spectrum of linear excitations, i.e., polaritons, consists of two branches separated by a relatively wide forbidden band. In the nonlinear regime, the dispersion relation of the carrier wave is determined by soliton width that is controlled by the reciprocal qubit frequency. The separate dispersion curves lie within the polariton forbidden band. Soliton transparency requires that the carrier wave frequency exceeds a threshold value; the latter depends strongly on the pulse width. We find that for pulses with widths ranging from ultrashort to an intermediate limit, the threshold is of the order of the gap frequency value in the photon spectrum. For wider pulses, the threshold frequency gradually decreases to values that are toward the edge of the polariton lower band, provided the soliton width is larger than a critical value. In the overcritical regime, the bandgap appears in the spectrum of the soliton carrier wave, while a twin transparency window appears in the soliton pulse dispersion law. A possible experimental observation of the predicted effects within the proposed setup would be of interest in understanding the properties of self-induced transparency in general and applications in the design of quantum technological devices.

我们从理论上研究了电磁脉冲通过一个无限的一维耦合光学微腔阵列的透明度,这些微腔均匀地填充了超导量子比特(每个腔一个)。两种类型的混合物质光波,即极化子和自激透明孤子,控制着这些介质中电磁辐射的透明度。线性激发的谱,即极化,由两个分支组成,由一个相对较宽的禁带分开。在非线性状态下,载波的色散关系由由互易量子比特频率控制的孤子宽度决定。分离的色散曲线位于极化子禁带内。孤子透明要求载波频率超过一个阈值;后者在很大程度上取决于脉冲宽度。我们发现,对于宽度从超短到中间极限的脉冲,阈值是光子光谱中间隙频率值的数量级。对于较宽的脉冲,如果孤子宽度大于临界值,则阈值频率逐渐减小到极化子下带的边缘。在过临界状态下,孤子载波谱出现带隙,孤子脉冲色散规律出现双透明窗口。在提出的装置中对预测效应进行可能的实验观察,将有助于理解自诱导透明的一般性质以及在量子技术器件设计中的应用。
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引用次数: 0
Next-generation reservoir computing for dynamical inference. 下一代油藏动态推理计算。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0302319
Rok Cestnik, Erik A Martens

We present a simple and scalable implementation of next-generation reservoir computing (NGRC) for modeling dynamical systems from time-series data. The method uses a pseudorandom nonlinear projection of time-delay embedded inputs, allowing the feature-space dimension to be chosen independently of the observation size and offering a flexible alternative to polynomial-based NGRC projections. We demonstrate the approach on benchmark tasks, including attractor reconstruction and bifurcation diagram estimation, using partial and noisy measurements. We further show that small amounts of measurement noise during training act as an effective regularizer, improving long-term autonomous stability compared to standard regression alone. Across all tests, the models remain stable over long rollouts and generalize beyond the training data. The framework offers explicit control of system state during prediction, and these properties make NGRC a natural candidate for applications such as surrogate modeling and digital-twin applications.

我们提出了一种简单且可扩展的下一代油藏计算(NGRC)实现,用于从时间序列数据中建模动态系统。该方法使用时延嵌入输入的伪随机非线性投影,允许独立于观测大小选择特征空间维度,并提供基于多项式的NGRC投影的灵活替代方案。我们使用部分和噪声测量在基准任务上演示了该方法,包括吸引子重构和分岔图估计。我们进一步表明,与单独的标准回归相比,训练过程中少量的测量噪声作为有效的正则化器,提高了长期的自主稳定性。在所有测试中,模型在长时间的部署中保持稳定,并且泛化到训练数据之外。该框架在预测过程中提供了对系统状态的显式控制,这些特性使NGRC成为代理建模和数字孪生应用等应用的自然候选者。
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引用次数: 0
Effects of T-type and L-type calcium currents on synchronized activity patterns in a model subthalamo-pallidal network. t型和l型钙电流对模型丘脑下-苍白质网络同步活动模式的影响。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0297677
Choongseok Park, Leonid L Rubchinsky, Sungwoo Ahn

Synchronized rhythmic oscillatory activity in the beta frequency band in the basal ganglia (BG) is a hallmark of Parkinson's disease (PD). Recent experiments and theoretical studies have demonstrated the crucial roles of T-type and L-type calcium currents in shaping the activity patterns of subthalamic nucleus (STN) neurons. However, the role of these currents in the generation of synchronized activity patterns in BG networks involving STN is still unknown. In this study, using an STN model incorporating T-type and L-type calcium currents, we examined how these currents shape the patterns of neural activity in a subthalamo-pallidal network, including network dynamics in response to periodic external inputs. The dynamics were studied in relation to the network connectivity parameters-modulated by dopamine (depleted in PD's BG)-and compared with the properties of the temporal patterning of synchronous neural activity previously observed in the experimental studies with Parkinsonian patients. Stronger T-type current enhanced post-inhibitory rebound bursting and expanded synchronized rhythmic activity, reducing the range of intermittent synchrony and increasing resistance to external entrainment. Stronger L-type current prolonged STN bursts, promoted intermittent synchrony over a wide range of input amplitudes, and sustained beta oscillations, suggesting a potential role in the pathophysiology of PD. These results highlight the interplay between intrinsic cellular properties, synaptic parameters, and external inputs in shaping pathological synchronized rhythms in BG networks. Understanding these network mechanisms may advance the understanding of Parkinsonian rhythmogenesis and further assist in finding ways to modulate and suppress pathological rhythms.

基底神经节(BG) β频段同步节律性振荡活动是帕金森病(PD)的标志。最近的实验和理论研究已经证明了t型和l型钙电流在形成丘脑下核(STN)神经元活动模式中的重要作用。然而,这些电流在涉及STN的BG网络中产生同步活动模式中的作用仍然未知。在这项研究中,我们使用了一个包含t型和l型钙电流的STN模型,研究了这些电流如何塑造丘脑下-pallidal网络中的神经活动模式,包括响应周期性外部输入的网络动力学。我们研究了与网络连接参数相关的动态——由多巴胺调节(PD’s BG耗竭)——并与之前在帕金森病患者实验研究中观察到的同步神经活动的时间模式进行了比较。更强的t型电流增强抑制后反弹爆发,扩大同步节奏活动,减少间歇同步范围,增加对外部夹带的阻力。较强的l型电流延长了STN爆发,促进了大范围输入振幅的间歇同步,并持续了β振荡,提示其在PD的病理生理中可能起作用。这些结果强调了内在细胞特性、突触参数和外部输入在形成BG网络病理同步节律中的相互作用。了解这些网络机制可以促进对帕金森节律发生的理解,并进一步帮助找到调节和抑制病理节律的方法。
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引用次数: 0
Fractional reaction-diffusion modeling and machine learning for vegetation pattern analysis in Junggar Basin under climate change. 气候变化下准噶尔盆地植被格局分式反应-扩散模型与机器学习分析
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0285845
Yimamu Maimaiti, Shanwei Li, Jianping Zhao

This study investigates the mechanistic effects of vegetation physiological processes and develops a refined vegetation-climate dynamic model with a fractional-in-space diffusion model. The model comprehensively integrates key climatic factors, such as precipitation, temperature, and CO2, to examine the impact of climate change on the evolution of vegetation patterns in the Junggar Basin. Through analysis, we find an inverse relation between the fractional-order coefficient and the size of the Turing instability domain. In addition, performing numerical simulations using real data from the Junggar Basin region, the results show that the interaction between heat stress and the effect of water and CO2 fertilization significantly affect vegetation growth. What is more, the future vegetation growth under different climate scenarios is predicted based on the current scenario and three climate scenarios from the Coupled Model Intercomparison Project Phase 6. We harness the predictive capabilities of machine learning algorithms to forecast changes in the current scenarios. The numerical results show that the current and the SSP1-2.6 scenarios are the favorable climate scenario for vegetation growth. In contrast, the SSP2-4.5 and SSP5-8.5 scenarios suppress vegetation growth and the SSP5-8.5 scenario exhibits the fastest rate of desertification.

研究了植被生理过程的机理作用,建立了基于空间分数扩散模型的精细植被-气候动力学模型。该模式综合了降水、温度、CO2等关键气候因子,考察了气候变化对准噶尔盆地植被格局演变的影响。通过分析,我们发现分数阶系数与图灵不稳定域的大小成反比关系。此外,利用准噶尔盆地实测数据进行数值模拟,结果表明,热胁迫与水分和CO2施肥效应的交互作用对植被生长有显著影响。基于耦合模式比对项目第6阶段的当前情景和3种气候情景,对未来不同气候情景下的植被生长进行了预测。我们利用机器学习算法的预测能力来预测当前场景的变化。结果表明,当前情景和SSP1-2.6情景是植被生长的有利气候情景。相反,SSP2-4.5和SSP5-8.5情景抑制植被生长,SSP5-8.5情景荒漠化速度最快。
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引用次数: 0
Complex dynamics induced by multiple timescales in a Wilson-Cowan model with homeostatic plasticity. 具有稳态塑性的Wilson-Cowan模型中多时间尺度诱导的复杂动力学。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2026-01-01 DOI: 10.1063/5.0294009
Ke He, Sue Ann Campbell, Shenquan Liu

Homeostatic adjustment of synaptic weights is important to prevent runaway excitation in neural populations, and it occurs on a slower timescale than the timescale of neural activity. Homeostatic plasticity in neural mass models can induce complex dynamical behaviors, including mixed-mode oscillations (MMOs) and chaos. In this paper, we investigate dynamical mechanisms by studying a single-node Wilson-Cowan model with homeostatic plasticity, which has three timescales associated with the activities of the excitatory/inhibitory (E/I) populations and the homeostatic connection weight, WI, from the I to the E population. We study how the relative timescale separations induce various dynamical behaviors. Analysis in two-timescale settings unveils two typical mechanisms underlying transitions. (1) Considering E as fast and the other variables as slow, canard-induced MMOs due to the presence of a folded node are observed. Bifurcations of folded singularities, including type II folded saddle-node and degenerate folded node, explain the dynamical transitions. (2) Considering WI as slow and E/I as fast, period-doubling cascades and canard explosion, induced by a degenerate folded point, explain the dynamical transitions. Extending to a three-timescale framework introduces interactions between singularities defined in the two-timescale settings and enables a more detailed description of the dynamics. Folded singularities in the three-timescale setting determine the structure of singular orbits. The degenerate folded point in the 2F/1S case determines the transition between MMOs and relaxation oscillation. This paper provides a comprehensive understanding of the role of three timescales in this single-node system and highlights how the connection weights between populations induce complex dynamical behaviors.

突触重量的内稳态调节对于防止神经群中的失控兴奋是重要的,它发生在一个比神经活动的时间尺度更慢的时间尺度上。神经质量模型的自稳态可塑性可诱发复杂的动力学行为,包括混合模振荡和混沌。在本文中,我们通过研究具有稳态可塑性的单节点Wilson-Cowan模型来研究动态机制,该模型具有三个时间尺度,与兴奋/抑制(E/I)群体的活动和从I到E群体的稳态连接权WI相关。我们研究了相对时标分离如何诱发各种动力学行为。在两个时间尺度设置下的分析揭示了两个典型的转换机制。(1)考虑E为快,其他变量为慢,观察到由于折叠节点的存在而引起的鸭鸭诱导mmo。折叠奇异点的分岔,包括II型折叠鞍节点和简并折叠节点,解释了动力学转变。(2)考虑WI为慢速,E/I为快,由简并折叠点引起的倍周期级联和鸭式爆炸可以解释动力学转变。扩展到三个时间尺度框架引入了在两个时间尺度设置中定义的奇点之间的相互作用,并允许对动力学进行更详细的描述。三时间尺度下的折叠奇点决定了奇异轨道的结构。在2F/1S的情况下,简并折叠点决定了mmo和弛豫振荡之间的过渡。本文全面理解了三个时间尺度在单节点系统中的作用,并强调了种群之间的连接权重如何诱导复杂的动态行为。
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引用次数: 0
Self-organizing network simulation of cardiac contraction dynamics. 心脏收缩动力学的自组织网络模拟。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2025-12-01 DOI: 10.1063/5.0305451
Runsang Liu, Hui Yang

Self-organizing network encodes and resembles structural geometry in the heart, offering a new pathway to study cardiac simulation. Hence, we have leveraged the sparsity of an adjacency matrix to design novel simulations of cardiac electrical dynamics on the self-organizing network. However, very little has been done to investigate network simulation of mechanical contraction dynamics. As a vertical step, this paper presents a new self-organizing network methodology for simulation modeling of cardiac contraction dynamics. To this end, we propose to model the self-organizing network as an interconnected spring-mass-damper system and further solve networked dynamic equations to simulate the orchestrated dynamics of mechanical contractions. The proposed methodology is evaluated and illustrated on both 2D cardiac tissues and the 3D heart. Experimental results show that the proposed methodology not only effectively models contraction dynamics in excitable media, but can also be flexibly extended to the whole heart.

自组织网络编码和模拟心脏的几何结构,为心脏模拟研究提供了新的途径。因此,我们利用邻接矩阵的稀疏性在自组织网络上设计了新的心脏电动力学模拟。然而,对机械收缩动力学的网络模拟研究很少。作为一个垂直的步骤,本文提出了一种新的自组织网络方法来模拟心脏收缩动力学。为此,我们建议将自组织网络建模为一个相互连接的弹簧-质量-阻尼系统,并进一步求解网络动力学方程来模拟机械收缩的协调动力学。所提出的方法在二维心脏组织和三维心脏上进行了评估和说明。实验结果表明,该方法不仅可以有效地模拟可激发介质中的收缩动力学,而且可以灵活地扩展到整个心脏。
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引用次数: 0
Synchronization transition via rhythmic states in the four-dimensional Kuramoto model with isoclinic rotations. 等斜旋转四维Kuramoto模型中节律态的同步跃迁。
IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED Pub Date : 2025-12-01 DOI: 10.1063/5.0303399
Wei Zou, Xiaoting Zhang, Jürgen Kurths

In this work, we are devoted to examining the phase transition to synchronization in the four-dimensional Kuramoto model with isoclinic rotations, where the rotation rate 4×4 antisymmetric matrix of each uncoupled agent is generated by a real three-dimensional vector. We uncover that the transition from incoherence to partial synchronization is mediated by time-dependent rhythmic states as the strength of coupling increases. The incoherent state is observed for a coupling strength below a certain threshold. Subsequently, a time-dependent rhythmic state appears as further increasing the strength of coupling, which persists for a pronounced interval of coupling strength. For a sufficiently large coupling strength, the system finally transits to partially locked states, where the generalized order parameter goes to a nontrivial fixed point. Via employing a higher-dimensional Ott-Antonsen ansatz in the thermodynamic limit of infinite system size, we theoretically establish that the uniformly incoherent state loses its stability via Hopf bifurcation at the critical coupling strength, which signals the emergence of a rhythmic state. We also obtain a self-consistency equation of the order parameter of the model undergoing partially locked states, from which the degree of coherence of the system at a sufficiently large coupling strength is theoretically predicted by two parametrized expressions. Our theoretical results agree very well with the results from our numerical simulations of the model with a sufficiently large but finite number of agents.

在这项工作中,我们致力于研究具有等斜旋转的四维Kuramoto模型中的相变到同步,其中每个解耦剂的旋转速率4×4反对称矩阵由实三维矢量生成。我们发现,随着耦合强度的增加,从非相干到部分同步的转变是由时间依赖的节奏状态介导的。当耦合强度低于一定阈值时,观察到非相干态。随后,随着耦合强度的进一步增加,一种时间依赖的节奏状态出现,这种状态持续一段明显的耦合强度间隔。当耦合强度足够大时,系统最终过渡到部分锁定状态,其中广义序参量趋于一个非平凡不动点。在无限系统尺寸的热力学极限下,我们利用高维的奥特-安东森分析,从理论上证明了均匀非相干态在临界耦合强度下通过Hopf分岔失去稳定性,这标志着节奏态的出现。得到了部分锁定状态下系统序参量的自洽方程,用两个参数化表达式从理论上预测了系统在足够大的耦合强度下的相干度。我们的理论结果与我们对具有足够大但有限数量的主体的模型的数值模拟结果吻合得很好。
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引用次数: 0
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