Dynamical Systems Theory Compared to Game Theory: The Case of the Salamis’s Battle

In this paper, we present an innovative non–linear, discrete, dynamical system trying to model the historic battle of Salamis between Greeks and Persians. September 2020 marks the anniversary of the 2500 years that have passed since this famous naval battle which took place in late September 480 B.C. The suggested model describes very well the most effective strategic behavior between two participants during a battle (or in a war). Moreover, we compare the results of the Dynamical Systems analysis to Game Theory, considering this conflict as a “war game”.

Capacity planning of hydro-wind-solar hybrid power systems considering hydropower forbidden zones

In the capacity planning of hydro-wind-solar power systems(CPHPS),it is crucial to use flexible hydropower to complement the variable wind-solar power.Hydropower units must be operated such that they avoid specific restricted operation zones,that is,forbidden zones(FZs),to avoid the risks associated with hydropower unit vibration.FZs cause limitations in terms of both the hydropower generation and flexible regulation in the hydro-wind-solar power systems.Therefore,it is essential to consider FZs when determining the optimal wind-solar power capacity that can be compensated by the hydropower.This study presents a mathematical model that incorporates the FZ constraints into the CPHPS problem.Firstly,the FZs of the hydropower units are converted into those of the hydropower plants based on set theory.Secondly,a mathematical model was formulated for the CPHPS,which couples the FZ constraints of hydropower plants with other operational constraints(e.g.,power balance constraints,new energy consumption limits,and hydropower generation functions).Thirdly,dynamic programming with successive approximations is employed to solve the proposed model.Lastly,case studies were conducted on the hydro-wind-solar system of the Qingshui River to demonstrate the effectiveness of the proposed model.

Use of Dynamical Systems Modeling to Hybrid Cloud Database

In the article, an experiment is aimed at clarifying the transfer efficiency of the database in the cloud infrastructure. The system was added to the control unit, which has guided the database search in the local part or in the cloud. It is shown that the time data acquisition remains unchanged as a result of modification. Suggestions have been made about the use of the theory of dynamic systems to hybrid cloud database. The present work is aimed at attracting the attention of specialists in the field of cloud database to the apparatus control theory. The experiment presented in this article allows the use of the description of the known methods for solving important practical problems.

Developmental Routines of Oral English Ability for English Major Students:Based on Complex and Dynamic Systems Theory

This study employs a Q methodology to explore the developmental routines of oral English ability for 12 English major students in China inspired by Complex and Dynamic Systems Theory(CDST).The data analysis suggests the next findings:(1)two developmental patterns emerge as the gradual improvement and the strong phase shift influenced by internal and external factors for interactions among different subsystems;(2)guided by CDST,the study proves the importance of self-organization and initial condition in previous studies.According to the above findings,It is highly suggested for teachers to form a holistic view of students’oral English development concerning the non-linear characteristic and individual differences.

Evaluation of the Validity of Chaos Theory Based on Systems Thinking for Non-Physicists

Chaos theory was born in the 18th century, physicists still solve the nonlinear dynamic systematic problems within closed-loop systems such as ecosystems, three-body problems involving complexity, and others. Moreover, it has been resolved these problems based on logical thinking using logical solutions with algebra and statistics such as chaos theory. The reason is determinism. Nevertheless, other scientists do not welcome the old chaos theory because the chaos theory is very imperfect and vague. Amazingly, in 2021, there is emerged, and an advanced and systematic solution based on system thinking;it was resolved by a non-physicist on behalf of physicists through interdisciplinary science and it is more perfect than the old chaos theory. Therefore, it is similar to the New World discovered by Columbus. This paper will prove that the existing chaos theory is invalid as a new solution emerges. Nevertheless, current physicists avoid approaching this study as much as possible. Therefore, other scientists have no reason to follow their invalid chaos theory unless physicists prove the validity of chaos theory.

THE COUPLING DYNAMICAL MODELING THEORY OF FLEXIBLE MULTIBODY SYSTEM

Based on the deformation theory of elastic beams, the coupling effect between the coupling displacements of a point on the middle line of beam and large overall motion is presented. The 'coupling matrix library' and Jourdain's variation principle and single direction recursive formulation method are used to establish the general coupling dynamical equations of flexible multibody system. Two typical examples show the coupling effect between coupling displacements and large overall motion on the dynamics of flexible multibody system consisting of beams.

Linearized Controller Design for the Output Probability Density Functions of Non-Gaussian Stochastic Systems

This paper presents a linearized approach for the controller design of the shape of output probability density functions for general stochastic systems. A square root approximation to an output probability density function is realized by a set of B-spline functions. This generally produces a nonlinear state space model for the weights of the B-spline approximation. A linearized model is therefore obtained and embedded into a performance function that measures the tracking error of the output probability density function with respect to a given distribution. By using this performance function as a Lyapunov function for the closed loop system, a feedback control input has been obtained which guarantees closed loop stability and realizes perfect tracking. The algorithm described in this paper has been tested on a simulated example and desired results have been achieved.

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.

Foundations and Applications of Information Systems Dynamics

Although numerous advances have been made in information technology in the past decades,there is still a lack of progress in information systems dynamics(ISD),owing to the lack of a mathematical foundation needed to describe information and the lack of an analytical framework to evaluate information systems.The value of ISD lies in its ability to guide the design,development,application,and evaluation of largescale information system-of-systems(So Ss),just as mechanical dynamics theories guide mechanical systems engineering.This paper reports on a breakthrough in these fundamental challenges by proposing a framework for information space,improving a mathematical theory for information measurement,and proposing a dynamic configuration model for information systems.In this way,it establishes a basic theoretical framework for ISD.The proposed theoretical methodologies have been successfully applied and verified in the Smart Court So Ss Engineering Project of China and have achieved significant improvements in the quality and efficiency of Chinese court informatization.The proposed ISD provides an innovative paradigm for the analysis,design,development,and evaluation of large-scale complex information systems,such as electronic government and smart cities.

Theory of Dynamic Interactions: The Flight of the Boomerang

We propose a new interpretation of the dynamic behavior of the boomerang and, in general, of the rigid bodies exposed to simultaneous non-coaxial rotations. We have developed a new rotational non-inertial dynamics hypothesis, which can be applied to understand both the flight of the boomerang as well as celestial mechanics. The boomerang is a particularly significant, intriguing and widely known case of bodies in rotation. We have analyzed the velocity and acceleration fields generated when rigid bodies are exposed to successive torques, in order to assess new criteria for this speed coupling. In this context, reactions and inertial fields that cannot be justified by means of classical mechanics take place. Accordingly, we propose a new Theory of Dynamic Interactions. We believe that the results obtained will enable us to conceive a new perspective in dynamics, unknown to date. After carrying out ample research, we have come to the conclusion that there still exists an unstructured scientific area in non-inertial dynamics systems subject to rotational accelerations. The aim of this paper is to present information of the surprising results obtained and to attract interest in research into dynamic field systems accelerated by rotation, and the multiple and remarkable scientific applications arising thereof. We further propose the boomerang as a clear example of the application of the Theory of Dynamic Interactions.

Theory of Dynamic Interactions: The Flight of the Boomerang II

On Volume 2, Number 7, June 2014 of this Journal of Applied Mathematics and Physics, I proposed a new interpretation of the dynamic behavior of the boomerang and, in general, of the rigid bodies exposed to simultaneous non-coaxial rotations. I proposed the boomerang as a paradigmatic example of bodies in rotation. Accordingly, I propose a new Theory of Dynamic Interactions. The aim of this paper is to present an audiovisual of the Theory of Dynamic Interactions, and the dynamic behavior of the boomerang, as an extension of the referred paper, asserting that the boomerang is a clear example of the application of this theory.

Theory of Dynamic Interactions: Laws of Motion

The aim of this paper is to present the laws of motion that can be derived from the Theory of Dynamic Interactions, and of its multiple and significant scientific applications. Based on a new interpretation on the behaviour of rigid bodies exposed to simultaneous non-coaxial rotations, we have developed a hypothesis regarding the dynamic behaviour of these bodies. From these hypotheses and following the observation of the behaviour of free bodies in space, we have developed axioms and a mathematical-physical model. Consequently, we have deduced a movement equation, coherent with the hypotheses and the observed behaviour. This dynamic model, in the case of rigid solid bodies or systems, allows putting forward a series of laws and corollaries in relation to its dynamic performance. These laws have subsequently been confirmed by experimental tests. The whole of this research constitutes a rational and conceptual structure which we have named Theory of Dynamic Interactions (TID). This logical deductive system allows predicting the behaviour of solid bodies subject to multiple accelerations by rotation. In the conclusions, we underline that coherence has been obtained between the principles and axioms, the developed physical-mathematical model, the obtained movement equation, the deduced laws and the realised experimental tests.

An improvement on measure methods of the complexity theory and its applications

A new method is proposed to transform the time series gained from a dynamic system to a symbolic series which extracts both overall and local information of the time series. Based on the transformation, two measures are defined to characterize the complexity of the symbolic series. The measures reflect the sensitive dependence of chaotic systems on initial conditions and the randomness of a time series, and thus can distinguish periodic or completely random series from chaotic time series even though the lengths of the time series are not long. Finally, the logistic map and the two-parameter Henon map are studied and the results are satisfactory.

Time/Space and Inertial System Reconsidered Based on the Adaptive Dynamical View

We have succeeded in 2-slit interference simulation by assuming that a travelling particle interacts with its environment, getting information on the environmental condition according to the adaptive dynamics by Ohya, thus proposed the possibility that the entanglement comes from the interaction with the environment (Ando et al., 2023). This concept means that there should be no isolated or inertial system other than our unique universe space. Taking this message into account and assuming that the signal velocity is constant against our unique universe space, we reconsidered the inertial system and relativity theory by Galilei and Einstein and found several misunderstandings and errors. Time delay and Lorentz shrinkage were derived similarly to the prediction by special relativity theory, but Lorentz transformation and 4-dimensional time/space view were not. They must have implicitly and unconsciously assumed that any signals transfer information without giving any influences to any systems different from our adaptive dynamical view. We propose that their relativity theories should be reinterpreted in view of adaptive dynamics.

相对论Birkhoff系统的Noether理论

给出相对论Pfaff -Birkhoff原理和相对论Birkhoff方程 .定义相对论Birkhoff系统的无限小变换生成元 ,根据在无限小变换下微分变分原理的不变性 ,得到相对论Birkhoff系统的Noether定理和Noether逆定理 .

基于非合作博弈论的多小区OFDMA系统动态资源分配算法研究

该文采用非合作博弈论的方法研究了多小区OFDMA系统中的动态资源分配问题,首先将各基站的发射功率平均分配给各子载波,然后由所有小区在每个子载波上独立地进行资源分配博弈,给出了用户调度与功率分配联合博弈框架。为了进一步简化,将用户调度和资源分配分开完成,通过将信道增益引入到定价函数中,提出了一种新的定价机制,建立了用户确定时的非合作功率分配博弈模型,分析了其纳什均衡的存在性和唯一性,并设计了具体的博弈算法。仿真结果表明,所提算法在保证吞吐量性能的同时,进一步提升了系统的公平性。

3-DOF混联机构的动力学建模与仿真分析

提出一种新型三自由度混联机构,运用螺旋理论分析了该机构的机构学原理,计算了机构自由度。以多刚体系统动力学理论为基础,建立了该并联机构的多体系统动力学模型,在此基础上开展了该机构正向运动学、逆向运动学及动力学的仿真研究。结果表明:在所设计的的构型及尺度下,机构存在非线性的输入输出关系;在Z轴方向一定的情形下,X方向最大运行角度为-15°,Y方向最大运行角度为-17°;从机构的加速度及速度运动曲线来看,机构不存在明显的刚性冲击。

Birkhoff系统动力学的研究进展

提出一个新力学———Ｂｉｒｋｈｏｆ系统动力学的基本理论框架，介绍近年的研究成果。

复杂产品系统后发追赶驱动因素研究——基于程序化扎根与系统动力学融合方法

复杂产品系统领域的追赶历程表明,后发者能否成功实现追赶受到多重因素的共同驱动,已有研究忽视了不同因素在追赶过程中的差异化作用,导致后发者难以把握不同追赶阶段的关键驱动因素,从而影响追赶策略的制定。为此,以中国大飞机、核电以及高铁为研究对象,运用程序化扎根方法识别复杂产品系统后发追赶驱动因素,构建复杂产品系统后发追赶驱动因素系统动力学模型并进行仿真。研究发现,中国复杂产品系统处于“三跑并行”局面,不同后发追赶阶段存在差异化关键驱动因素。在跟随阶段,举国体制、二次创新、集成创新是关键驱动因素;在并行阶段,制度型市场开拓、自主研发、集成创新是关键驱动因素;在超越阶段,制度型市场规模、自主研发、举国体制是关键驱动因素。研究结论可为中国不同追赶阶段复杂产品系统后发追赶策略制定提供理论指导。

人类动作发展的变化与适应:理论基础与实践走向

人类从胎儿开始,动作行为就以自发的神经活动为基础,脑干和脊髓的神经网络活动受到脊髓上活动的调节。脊髓上活动首先由皮层板引起,随之引起动作的变化,起初这些动作的变化是为探索服务,其相关的传入信息主要用于塑造神经系统的发育。随后,动作的变化逐渐开始适应,随着年龄和试错探索的增加,婴幼儿适应后的有效动作发展能力得到了显著的提升。文章从人类大脑进化与动作发展的某些启示出发,围绕动态系统理论(dynamic systems theory, DST)和神经元群选择理论(neuronal group selection theory, NGST)进行理论溯源,提出动作发展的循证轨迹。在探索理论的同时,文章对新生儿可穿戴式运动监测设备的研制,胎动(fetal movement, FM)的监测与应用以及基本动作技能(fundamental Motor Skill, FMS)的发展与学习三个应用研究领域进行了局部展望,这些领域着眼于“脑与动作的双向构建”,将有助于我们了解人类动作发展与脑科学之间的联系,从而期望开辟新的研究领域来更好地理解动作发展的内生机制。