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Chaotic van der Pol Oscillator Control Algorithm Comparison 混沌范德波尔振荡器控制算法比较
Pub Date : 2023-03-19 DOI: 10.3390/dynamics3010012
Lauren Ribordy, Timothy Sands
The damped van der Pol oscillator is a chaotic non-linear system. Small perturbations in initial conditions may result in wildly different trajectories. Controlling, or forcing, the behavior of a van der Pol oscillator is difficult to achieve through traditional adaptive control methods. Connecting two van der Pol oscillators together where the output of one oscillator, the driver, drives the behavior of its partner, the responder, is a proven technique for controlling the van der Pol oscillator. Deterministic artificial intelligence is a feedforward and feedback control method that leverages the known physics of the van der Pol system to learn optimal system parameters for the forcing function. We assessed the performance of deterministic artificial intelligence employing three different online parameter estimation algorithms. Our evaluation criteria include mean absolute error between the target trajectory and the response oscillator trajectory over time. Two algorithms performed better than the benchmark with necessary discussion of the conditions under which they perform best. Recursive least squares with exponential forgetting had the lowest mean absolute error overall, with a 2.46% reduction in error compared to the baseline, feedforward without deterministic artificial intelligence. While least mean squares with normalized gradient adaptation had worse initial error in the first 10% of the simulation, after that point it exhibited consistently lower error. Over the last 90% of the simulation, deterministic artificial intelligence with least mean squares with normalized gradient adaptation achieved a 48.7% reduction in mean absolute error compared to baseline.
阻尼范德波尔振荡器是一个混沌非线性系统。初始条件下的微小扰动可能导致轨迹的大不相同。通过传统的自适应控制方法很难控制或强制范德波尔振荡器的行为。将两个范德波尔振荡器连接在一起,其中一个振荡器(驱动器)的输出驱动其伙伴(响应器)的行为,是一种经过验证的控制范德波尔振荡器的技术。确定性人工智能是一种前馈和反馈控制方法,它利用已知的范德波尔系统物理特性来学习强制函数的最优系统参数。我们使用三种不同的在线参数估计算法评估确定性人工智能的性能。我们的评估标准包括目标轨迹和响应振荡器轨迹之间随时间的平均绝对误差。有两种算法在必要的条件下表现得比基准更好。具有指数遗忘的递归最小二乘总体上具有最低的平均绝对误差,与没有确定性人工智能的前馈相比,误差减少了2.46%。虽然归一化梯度自适应的最小均方差在模拟的前10%具有较差的初始误差,但在此之后,其误差始终较低。在最后90%的模拟中,具有最小均方差和归一化梯度适应的确定性人工智能与基线相比,平均绝对误差降低了48.7%。
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引用次数: 0
Existence for Nonlinear Fourth-Order Two-Point Boundary Value Problems 非线性四阶两点边值问题的存在性
Pub Date : 2023-03-13 DOI: 10.3390/dynamics3010010
R. Agarwal, Gabriela Mihaylova, P. Kelevedjiev
The present paper is devoted to the solvability of various two-point boundary value problems for the equation y(4)=f(t,y,y′,y″,y‴), where the nonlinearity f may be defined on a bounded set and is needed to be continuous on a suitable subset of its domain. The established existence results guarantee not just a solution to the considered boundary value problems but also guarantee the existence of monotone solutions with suitable signs and curvature. The obtained results rely on a basic existence theorem, which is a variant of a theorem due to A. Granas, R. Guenther and J. Lee. The a priori bounds necessary for the application of the basic theorem are provided by the barrier strip technique. The existence results are illustrated with examples.
本文研究方程y(4)=f(t,y,y ',y″,y )的各种两点边值问题的可解性,其中非线性f可以定义在有界集合上,并且需要在其定义域的适当子集上连续。所建立的存在性结果不仅保证了所考虑的边值问题的解,而且保证了具有合适符号和曲率的单调解的存在性。得到的结果依赖于一个基本存在定理,它是a . Granas, R. Guenther和J. Lee的定理的变体。障条技术提供了应用基本定理所必需的先验界。用实例说明了存在性结果。
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引用次数: 1
Search for Damped Oscillating Structures from Charged Pion Electromagnetic Form Factor Data 从带电介子电磁形状因子数据中搜索阻尼振荡结构
Pub Date : 2023-03-04 DOI: 10.3390/dynamics3010009
E. Bartoš, S. Dubnička, A. Dubničková
The damped oscillating structures recently revealed by a three parametric formula from the proton “effective” form factor data extracted of the measured total cross section σtotbare(e+e−→pp¯) still seem to have an unknown origin. The conjectures of their direct manifestation of the quark-gluon structure of the proton indicate that they are not specific only of the proton and neutron, but they have to be one’s own, similar to other hadrons. Therefore, the oscillatory structures from the charged pion electromagnetic form factor timelike data, extracted of the process e+e−→π+π− are investigated by using the same procedure as in the case of the proton. The analysis shows the appearance of the oscillating structures in the description of the charged pion electromagnetic form factor timelike data by three parametric formula with a rather large value of χ2/ndf, while the description of the data by the physically well-founded Unitary and Analytic model has not revealed any damped oscillating structures. From the obtained result on the most simple object of strong interactions, one can conclude that damped oscillating structures received from the “effective” proton form factor data are probably generated by a utilization of the improper three parametric formula which does not describe these data with sufficient precision.
从实测总截面σ tobare (e+e−→pp¯)中提取的质子“有效”形状因子数据,用一个三参数公式揭示的阻尼振荡结构似乎仍然有一个未知的起源。它们对质子的夸克-胶子结构的直接表现的推测表明,它们不仅是质子和中子所特有的,而且必须是一个人自己的,类似于其他强子。因此,从e+e−→π+π−过程中提取的带电介子电磁形状因子类时数据的振荡结构采用与质子相同的方法进行了研究。分析表明,在用χ2/ndf值较大的三参数公式描述带电介子电磁形状因子时型数据时,出现了振荡结构,而用物理上建立良好的酉解析模型描述数据时,没有发现任何阻尼振荡结构。从在最简单的强相互作用对象上得到的结果可以得出结论,从“有效”质子形状因子数据中得到的阻尼振荡结构可能是由利用不适当的三参数公式产生的,该公式不能足够精确地描述这些数据。
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引用次数: 1
Enhancing Bayesian Approaches in the Cognitive and Neural Sciences via Complex Dynamical Systems Theory 通过复杂动力系统理论增强认知和神经科学中的贝叶斯方法
Pub Date : 2023-03-01 DOI: 10.3390/dynamics3010008
Luis H. Favela, M. J. Amon
In the cognitive and neural sciences, Bayesianism refers to a collection of concepts and methods stemming from various implementations of Bayes’ theorem, which is a formal way to calculate the conditional probability of a hypothesis being true based on prior expectations and updating priors in the face of errors. Bayes’ theorem has been fruitfully applied to describe and explain a wide range of cognitive and neural phenomena (e.g., visual perception and neural population activity) and is at the core of various theories (e.g., predictive processing). Despite these successes, we claim that Bayesianism has two interrelated shortcomings: its calculations and models are predominantly linear and noise is assumed to be random and unstructured versus deterministic. We outline ways that Bayesianism can address those shortcomings: first, by making more central the nonlinearities characteristic of biological cognitive systems, and second, by treating noise not as random and unstructured dynamics, but as the kind of structured nonlinearities of complex dynamical systems (e.g., chaos and fractals). We provide bistable visual percepts as an example of a real-world phenomenon that demonstrates the fruitfulness of integrating complex dynamical systems theory in Bayesian treatments of perception. Doing so facilitates a Bayesianism that is more capable of explaining a number of currently out-of-reach natural phenomena on their own, biologically realistic terms.
在认知和神经科学中,贝叶斯主义是指源于贝叶斯定理的各种实现的概念和方法的集合,它是一种基于先验期望计算假设为真的条件概率的正式方法,并在面对错误时更新先验。贝叶斯定理已经被卓有成效地应用于描述和解释广泛的认知和神经现象(例如,视觉感知和神经群体活动),并且是各种理论(例如,预测处理)的核心。尽管取得了这些成功,但我们认为贝叶斯主义有两个相互关联的缺点:它的计算和模型主要是线性的,噪声被认为是随机的、非结构化的,而不是确定性的。我们概述了贝叶斯主义可以解决这些缺点的方法:首先,通过使生物认知系统的非线性特征更加集中,其次,通过将噪声不视为随机和非结构化的动力学,而是作为复杂动力系统(例如,混沌和分形)的结构化非线性。我们提供了双稳态视觉感知作为一个现实世界现象的例子,证明了在贝叶斯感知治疗中整合复杂动力系统理论的成果。这样做有利于贝叶斯主义,它更有能力解释一些目前遥不可及的自然现象,从生物学的现实角度来看。
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引用次数: 0
An Energy-Based Complex Brain Network Model—Part 1: Local Electrophysiological Dynamics 基于能量的复杂脑网络模型-第一部分:局部电生理动力学
Pub Date : 2023-02-20 DOI: 10.3390/dynamics3010007
Chunbin Yang, N. Shettigar, C. Suh
The human brain is a complex network of connected neurons whose dynamics are difficult to describe. Brain dynamics are the global manifestation of individual neuron dynamics and the synaptic coupling between neurons. Membrane potential is a function of synaptic dynamics and electrophysiological coupling, with the parameters of postsynaptic potential, action potential, and ion pump dynamics. By modelling synaptic dynamics using physical laws and the time evolution of membrane potential using energy, neuron dynamics can be described. This local depiction can be scaled up to describe mesoscopic and macroscopic hierarchical complexity in the brain. Modelling results are favorably compared with physiological observation and physically acquired action potential profiles as reported in the literature.
人脑是一个由相互连接的神经元组成的复杂网络,其动态难以描述。脑动力学是单个神经元动力学和神经元间突触耦合的全局表现。膜电位是突触动力学和电生理耦合的函数,参数包括突触后电位、动作电位和离子泵动力学。利用物理定律模拟突触动力学,利用能量模拟膜电位的时间演化,可以描述神经元动力学。这种局部描述可以扩展到描述大脑中观和宏观的层次复杂性。建模结果与文献中报道的生理观察和物理获得的动作电位剖面相比较是有利的。
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引用次数: 0
Dark Energy as a Natural Property of Cosmic Polytropes—A Tutorial 暗能量作为宇宙多元体的自然属性-教程
Pub Date : 2023-02-15 DOI: 10.3390/dynamics3010006
K. Kleidis, N. Spyrou
A conventional approach to the dark energy (DE) concept is reviewed and discussed. According to it, there is absolutely no need for a novel DE component in the universe, provided that its matter–energy content is represented by a perfect fluid whose volume elements perform polytropic flows. When the (thermodynamic) energy of the associated internal motions is taken into account as an additional source of the universal gravitational field, it compensates the DE needed to compromise spatial flatness in an accelerating universe. The unified model which is driven by a polytropic fluid not only interprets the observations associated with universe expansion but successfully confronts all the current issues of cosmological significance, thus arising as a viable alternative to the ΛCDM model.
回顾和讨论了暗能量(DE)概念的传统方法。根据它,宇宙中绝对不需要新的DE组分,只要它的物质-能量含量是由体积元进行多向流动的完美流体表示的。当相关内部运动的(热力学)能量被考虑为万有引力场的额外来源时,它补偿了在加速宇宙中妥协空间平坦性所需的DE。由多向性流体驱动的统一模型不仅解释了与宇宙膨胀有关的观测结果,而且成功地解决了当前所有具有宇宙学意义的问题,从而成为ΛCDM模型的可行替代方案。
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引用次数: 0
Complex Network Methods for Plastic Deformation Dynamics in Metals 金属塑性变形动力学的复杂网络方法
Pub Date : 2023-01-30 DOI: 10.3390/dynamics3010004
A. Kiv, A. Bryukhanov, V. Soloviev, A. Bielinskyi, T. Kavetskyy, D.A. Dyachok, I. Donchev, V. Lukashin
Plastic deformation of DC04 steel is regarded as a nonlinear, complex, irreversible, and self-organized process. The stress–strain time series analysis provided the possibility to identify areas of (quasi-)elastic deformation, plastic deformation, and necking. The latter two regions are the most informative. The area of inelastic deformation is reflected by collective, self-organized processes that lead to the formation of pores, and finally, the development of microcracks and a general crack as the cause of sample failure. Network measures for the quantitative assessment of the structural deformations in metals are proposed. Both spectral and topological measures of network complexity were found to be especially informative. According to our results, they can be used not only to classify the stages of plastic deformation, but also, they can be applied as a precursor of the material destruction process.
DC04钢的塑性变形是一个非线性的、复杂的、不可逆的、自组织的过程。应力-应变时间序列分析提供了识别(准)弹性变形、塑性变形和颈缩区域的可能性。后两个区域的信息最丰富。非弹性变形的面积反映在集体的、自组织的过程中,这些过程导致孔隙的形成,最后,微裂纹和一般裂纹的发展是试样破坏的原因。提出了定量评价金属结构变形的网络方法。发现网络复杂性的频谱和拓扑度量都是特别有用的。根据我们的研究结果,它们不仅可以用来对塑性变形的阶段进行分类,而且可以作为材料破坏过程的前兆。
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引用次数: 0
Acknowledgment to the Reviewers of Dynamics in 2022 感谢《动力》杂志2022年的审稿人
Pub Date : 2023-01-18 DOI: 10.3390/dynamics3010003
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引用次数: 0
Dynamical Invariant for Dissipative Systems via Complex Quantum Hydrodynamics 耗散系统的复杂量子流体力学动力学不变量
Pub Date : 2023-01-16 DOI: 10.3390/dynamics3010002
D. Schuch, M. Bonilla-Licea
For Hamiltonian systems with time-dependent potential, the Hamiltonian, and thus the energy, is no longer a constant of motion. However, for such systems as the parametric oscillator, i.e., an oscillator with time-dependent frequency ω(t), still, a dynamical invariant can be found that now has the dimension of action. The question, if such an invariant still exists after the addition of a dissipative friction force is analyzed for the classical as well as for the quantum mechanical case from different perspectives, particularly from that of a complex hydrodynamic formulation of quantum mechanics.
对于具有随时间变化的势的哈密顿系统,哈密顿量,也就是能量,不再是运动常数。然而,对于像参数振子这样的系统,即频率随时间变化ω(t)的振子,仍然可以找到一个具有作用维数的动态不变量。从不同的角度,特别是从量子力学的复杂流体力学公式的角度,分析了在加入耗散摩擦力后,这种不变量是否仍然存在的问题。
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引用次数: 0
Non-Equilibrium ϕ4 Theory in a Hierarchy: Towards Manipulating Holograms in Quantum Brain Dynamics 层次结构中的非平衡态ϕ4理论:在量子脑动力学中操纵全息图
Pub Date : 2023-01-04 DOI: 10.3390/dynamics3010001
Akihiro Nishiyama, Shigenori Tanaka, Jack A. Tuszynski
We describe non-equilibrium ϕ4 theory in a hierarchical manner to develop a method for manipulating coherent fields as a toy model of introducing control into Quantum Field Theory (QFT) of the brain, which is called Quantum Brain Dynamics (QBD). We begin with the Lagrangian density of ϕ4 model, where we adopt 2-Particle-Irreducible (2PI) effective action, and derive the Klein–Gordon equation of coherent fields with a damping term as an input–output equation proposed in areas of morphological computation or reservoir computing. Our analysis is extended to QFT in a hierarchy representing multiple layers covering cortex in a brain. We find that the desired target function is achieved via time-evolution in the Klein–Gordon equations in a hierarchy of numerical simulations when a signal in both the input and output prevails over noise in the intermediate layers. Our approach will be applied to control coherent fields in the systems (in a hierarchy) described in the QFT framework, with potential applications allowing the manipulation of quantum fields, especially holograms in QBD. We could then provide realistic physical degrees of freedom of a light–matter system in the contexts of quantum cognition and the associated free-energy principle.
我们以分层方式描述非平衡态的ϕ4理论,以开发一种操作相干场的方法,作为将控制引入大脑量子场论(QFT)的玩具模型,称为量子脑动力学(QBD)。我们从拉格朗日密度模型开始,其中我们采用2粒子不可约(2PI)有效作用,并推导出具有阻尼项的相干场的Klein-Gordon方程,作为形态学计算或库计算领域中提出的输入输出方程。我们的分析被扩展到QFT中的层次结构,表示覆盖大脑皮层的多层。我们发现,当输入和输出中的信号都优于中间层中的噪声时,期望的目标函数通过Klein-Gordon方程中的时间进化实现。我们的方法将被应用于控制QFT框架中描述的系统(在层次结构中)中的相干场,具有潜在的应用允许操纵量子场,特别是QBD中的全息图。然后,我们可以在量子认知和相关的自由能原理的背景下提供光-物质系统的实际物理自由度。
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引用次数: 4
期刊
Dynamics (Pembroke, Ont.)
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