On the relationship between uniqueness and stability in sum-aggregative,symmetric and general differentiable games

This article explores the relationship between uniqueness and stability in differentiable regular games, with a major focus on the important classes of sum-aggregative, two-player and symmetric games. We consider three types of popular dynamics, continuous-time gradient dynamics as well as continuous- and discrete-time best-reply dynamics, and include aggregate-taking behavior as a non-strategic behavioral variant. We show that while in general games stability conditions are only sufficient for uniqueness, they are likely to be necessary as well in models with sum-aggregative or symmetric payoff functions. In particular, a unique equilibrium always verifies the stability conditions of all dynamics if strategies are equilibrium complements, and this also holds for both continuous-time dynamics if strategies are equilibrium substitutes with bounded slopes. These findings extend to the case of aggregate-taking equilibria. We further analyze the stability relations between the various dynamics, and demonstrate that the restrictive nature of the discrete dynamics originates from simultaneity of adjustments. Asynchronous decisions or heterogeneous forward thinking may stabilize the adjustment process.     

Coupled problems in transient fluid and structural dynamics in nuclear engineering: Part 1: Safety problems solved by flow singularity methods

Some important problems in coupled fluid-structural dynamics which occur in safety investigations of liquid metal fast breeder reactors (LMFBR), light water reactors and nuclear reprocessing plants are discussed and a classification of solution methods is introduced. A distinction is made between the step by step solution procedure, where available computer codes in fluid and structural dynamics are coupled, and advanced simultaneous solution methods, where the coupling is carried out at the level of the fundamental equations. Results presented include the transient deformation of a two-row pin bundle surrounded by an infinite fluid field, vapour explosions in a fluid container and containment distortions due to bubble collapse in the pressure suppression system of a boiling water reactor. A recently developed simultaneous solution method is presented in detail. Here the fluid dynamics (inviscid, incompressible fluid) is described by a singularity method which reduces the three-dimensional fluid dynamics problem to a two-dimensional formulation. In this way the three-dimensional fluid dynamics as well as the structural (shell) dynamics can be described essentially by common unknowns at the fluid-structural interface. The resulting equations for the coupled fluid-structural dynamics are analogous to the equations of motion of the structural dynamics alone.     

Allee effects in a discrete-time SIS epidemic model with infected newborns

We extend the framework of Rios-Soto et al. (Contemporary Mathematics, 2006, 410, 297) to include both compensatory (contest competition) and overcompensatory (scramble competition) population dynamics with and without the Allee effect. We compute the basic reproductive number ?₀, and use it to predict the (uniform) persistence or extinction of the infective population, where the population dynamics are compensatory and the Allee effect is either present or absent. We also explore the relationship between the demographic equation and the epidemic process, where the total population dynamics are overcompensatory. In particular, we show that the demographic dynamics drive both the susceptible and infective dynamics. This is in contrast to the recent observations of Franke and Yakubu, that the demographic dynamics can be chaotic while the infective dynamics are oscillatory and non-chaotic in periodically-forced SIS epidemic models (Mathematical Biosciences, 2006, 204, 68).     

变质量非线性非完整系统相对运动动力学方程的积分方法

本文给出积分变质量非线性非完整系统相对于非惯性系动力学方程的梯度法,单分量法和场方法。首先,将这类问题的动力学方程表示为正则形式和场方程形式;然后,分别用梯度法,单分量法和场方法积分相应常质量完整系统相对于惯性系的动力学方程,并加上非完整约束对初始条件的限制而得到变质量非线性非完整系统相对于非惯性系动力学方程的解。     

Discrete-time Metapopulation Dynamics and Unidirectional Dispersal

The effects of unidirectional dispersal on single pioneer species discrete-time metapopulations where the pre-dispersal local patch dynamics are of the same (compensatory or overcompensatory) or mixed (compensatory and overcompensatory) types are studied. Single-species unidirectional metapopulation models behave as single-species single-patch models whenever all pre-dispersal local patch dynamics are compensatory and the dispersal rate is low. The pioneer species goes extinct in at least one patch when the dispersal rate is high, while it persists when the rate is low. Unidirectional dispersal can generate multiple attractors with fractal basin boundaries whenever the pre-dispersal local patch dynamics are overcompensatory, and is capable of altering the local patch dynamics in mixed systems from compensatory to overcompensatory dynamics and vice versa.     

Hybrid systems: Modelling and analysis using emergent dynamics

In this paper, we discuss modelling and analysis of hybrid systems with physical interaction dynamics. Such systems are typically considered complex and they are modelled using abstractions. Abstractions may, however, unintentionally exclude critical details, leading to partial or false results. Therefore, we study here use of a particle system in modelling and analysis. The novelty of the particle system is that it is designed to reveal interaction dynamics as emergent dynamics; thus, supporting analysis of complex and intricate interaction dynamics with acceptable modelling effort. As the main contribution, we formalize the particle system, and use it to model and analyze hybrid systems, both mechanical and biological, with nontrivial interaction dynamics.     

Multiple Attractors in Juvenile-adult Single Species Models

The role of age-structure and the Allee effect in generating multiple attractors in juvenile-adult single species single patch discrete-time models without dispersal are studied. In the presence of the Allee effect juvenile-adult single patch models support multiple attractors. However, in the absence of the Allee effect single attractors are supported when the dynamics are compensatory while multiple attractors are supported under overcompensatory dynamics. When the governing dynamics are compensatory, the boundaries of the basins of attraction have simple structure while complicated fractal basin boundaries are supported under overcompensatory dynamics.     

Automata in Groups and Dynamics and Induced Systems of PDE in Tropical Geometry

In this paper we develop a dynamical scaling limit from rational dynamics to automata in tropical geometry. We compare these dynamics and induce uniform estimates of their orbits. We apply these estimates to introduce a comparison analysis of theory of automata groups in geometric group theory with analysis of rational dynamics and some hyperbolic PDE systems. Frameworks of characteristic properties of automata groups are inherited to the corresponding rational or PDE dynamics. As an application we study the Burnside problem in group theory and translate the property as the infinite quasi-recursiveness in rational dynamics.     

非线性非完整系统Vacco动力学方程的积分方法*

本文给出积分非线性非完整系统Vacco动力学方程的积分方法.首先,将Vacco动力学方程表示为正则形式和场方程形式;然后,分别用梯度法,单分量法和场方法积分相应完整系统的动力学方程,并加上非完整约束对初条件的限制而得到非线性非完整系统Vacco动力学方程的解.     

Opinion convergence in the Krasnoshchekov model

In this paper, a rigorous mathematical analysis of the Krasnoshchekov model is presented. We have shown that in case a community does not contain any group of people having zero resistance to interpersonal influence, which are moreover isolated from the pressure of the rest of community, the Krasnoshchekov opinion readjustment procedure can be reduced to the Friedkin–Johnsen dynamics. In turn, if one repeats the Krasnoshchekov opinion updating rule, the corresponding dynamics forces individuals’ opinions to converge eventually to some terminal opinions, which are a consensus under the same conditions as in the French–Harary–DeGroot dynamics. Otherwise, the Krasnoshchekov dynamics exhibits patterns, which are much closer to the behavior of electrons in the superconductivity state.     

Projective dynamics and classical gravitation

We show that there exists a projective dynamics of a particle. It underlies intrinsically the classical particle dynamics as projective geometry underlies Euclidean geometry. In classical particle dynamics a particle moves in the Euclidean space subjected to a potential. In projective dynamics the position space has only the local structure of the real projective space. The particle is subjected to a field of projective forces. A projective force is not an element of the tangent bundle to the position space, but of some fibre bundle isomorphic to the tangent bundle. These statements are direct consequences of Appell’s remarks on the homography in mechanics, and are compatible with similar statements due to Tabachnikov concerning projective billiards. When we study Euclidean geometry we meet some particular properties that we recognize as projective properties. The same is true for the dynamics of a particle. We show that two properties in classical particle dynamics are projective properties. The fact that the Keplerian orbits close after one turn is a consequence of a more general projective statement. The fact that the fields of gravitational forces are divergence free is a projective property of these fields.      

Nonlinear Dynamics of the 3D Pendulum

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. 3D pendulum dynamics have been much studied in integrable cases that arise when certain physical symmetry assumptions are made. This paper treats the non-integrable case of the 3D pendulum dynamics when the rigid body is asymmetric and the center of mass is distinct from the pivot location. 3D pendulum full and reduced models are introduced and used to study important features of the nonlinear dynamics: conserved quantities, equilibria, relative equilibria, invariant manifolds, local dynamics, and presence of chaotic motions. The paper provides a unified treatment of the 3D pendulum dynamics that includes prior results and new results expressed in the framework of geometric mechanics. These results demonstrate the rich and complex dynamics of the 3D pendulum.     

具有Monod-Haldane功能反应的一类食物链模型的动力学行为

该文研究了一个由食饵种群、捕食者种群和杂食者种群所构成的食物链系统, 其捕食功能反应为Monod-Haldane功能反应. 应用定性分析和Hopf分支理论, 得到了该系统边界平衡点的全局稳定性和周期解存在性的判别准则. 为了概括和归类这个系统的全局动力学行为,该文得到了具有不同动力学行为的参数区域. 应用MATLAB软件,该文提供了一个例子来展示这些结论, 并且表明: 这个系统能够产生非常复杂的动力学行为.     

A study of the dynamics of the climate system of Northern Eurasia and the Arctic basin

The climate dynamics in Northern Eurasia under the conditions of global climate change is studied based on atmosphere-ocean coupled general circulation models. Feedbacks for some parameters of the atmosphere are assessed and analyzed. The role of the biosphere in the climate dynamics of the 21st century is investigated with allowance for the structure of the surface layer, vegetation layer, soil, and hydrology dynamics. Peculiarities of the dynamics of the North Atlantic and the Arctic Ocean are explored over periods pertaining to various phases of the North Atlantic Oscillation (NAO) index.     

种群模型在生物进化研究中的应用

介绍了进化动力学的基本知识和研究现状,把表型特征引入种群动力学模型,进而推导出进化适应动力学模型;总结了如何建立适应度函数以及分析研究进化动力学行为的一般理论和方法,并列举实例,模拟分析验证前面所陈述的理论方法,模拟结果说明收获对生物进化产生重要影响,并有效解释了物种多样性。     

Multi-period models for analyzing the dynamics of process improvement activities

Managing knowledge based resource capabilities has become very important in recent years and during a finite horizon it seems to be reasonable to develop the capabilities intensively at the beginning as one can utilize those over a longer period of time. With the help of multi-period models we check the validity of this idea and characterize the dynamics of development activities. The paper identifies the factors that shape these dynamics and from the behavior of these factors we conclude when the dynamics can be increasing or decreasing. We point out that in stable environment there is tendency for decreasing dynamics but future expectations can significantly modify this outcome. Relationships between the successful or less successful implementation of a business strategy and the dynamics of improvement activities are highlighted as well. For specific model structures explicit solutions are derived.     

微循环系统动力学综合数学模型研究(Ⅰ)——理论基础

根据微循环系统的生理情况,建立了微循环系统动力学非定常、非线性分布参数模型,包括血液动力学、间质动力学、淋巴动力学、蛋白质传输动力学、氧动力学、热量传输动力学和肌原性与代谢性调控过程,综合反映了它们之间的相互作用,并考虑了微动脉自律运动和血液非线性粘弹性的影响.几何模型是一个包括微动脉、开放与储备毛细血管、微静脉、初始淋巴管和微动静脉吻合支的简单网络.这种综合模型有助于临床数据的分析研究和“数值实验手段”的建立.     

Algoritmo compensador neuronal discreto de dinámica en robots móviles usando filtro de Kalman extendido

This paper presents the design of an algorithm based on neural networks in discrete time for its application in mobile robots. In addition, the system stability is analyzed and an evaluation of the experimental results is shown.The mobile robot has two controllers, one addressed for the kinematics and the other one designed for the dynamics. Both controllers are based on the feedback linearization. The controller of the dynamics only has information of the nominal dynamics (parameters). The neural algorithm of compensation adapts its behaviour to reduce the perturbations caused by the variations in the dynamics and the model uncertainties. Thus, the differences in the dynamics between the nominal model and the real one are learned by a neural network RBF (radial basis functions) where the output weights are set using the extended Kalman filter. The neural compensation algorithm is efficient, since the consumed processing time is lower than the one required to learning the totality of the dynamics. In addition, the proposed algorithm is robust with respect to failures of the dynamic controller. In this work, a stability analysis of the adaptable neural algorithm is shown and it is demonstrated that the control errors are bounded depending on the error of approximation of the neural network RBF. Finally, the results of experiments performed by using a mobile robot are shown to test the viability in practice and the performance for the control of robots.     

Chaos and Hyperchaos in Coupled Antiphase Driven Toda Oscillators

The dynamics of two coupled antiphase driven Toda oscillators is studied. We demonstrate three different routes of transition to chaotic dynamics associated with different bifurcations of periodic and quasi-periodic regimes. As a result of these, two types of chaotic dynamics with one and two positive Lyapunov exponents are observed. We argue that the results obtained are robust as they can exist in a wide range of the system parameters.     

Rotationless formulation for large deformations in flexible multibody dynamics

Especially for specific applications, such as contact problems, computer methods for flexible multibody dynamics that are able to treat large deformation phenomena are important. Classical formalisms for multibody dynamics are based on rigid bodies. Their extension to flexible multibody systems is typically restricted to linear elastic material behavior whereas large deformation phenomena are formulated in the framework of the nonlinear finite element method. In the talk we address computer methods that can handle large deformations in the context of multibody systems. In particular, the link between nonlinear continuum mechanics and multibody systems is facilitated by a specific formulation of rigid body dynamics [1]. It makes possible the incorporation of state-of-the-art computer methods for large deformation problems. In the talk we focus on the treatment of large deformation contact whithin flexible multibody dynamics [2]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)