Existence of periodic solutions of sublinear Hamiltonian systems

The variational method is used to obtain some existence theorems of periodic solutions of sublinear systems with or not with impacts under suitable growth conditions. Compared with normal systems, impact systems need additional conditions to ensure the existence of periodic bouncing solutions.     

Controlling chaotic orbits in mechanical systems with impacts

We stabilize desired unstable periodic orbits, embedded in the chaotic invariant sets of mechanical systems with impacts, by applying a small and precise perturbation on an available control parameter. To obtain such perturbation numerically, we introduce a transcendental map (impact map) for the dynamical variables computed just after the impacts. To show how to implement the method, we apply it to an impact oscillator and to an impact-pair system.     

Leaderless and leader-following consensus of multi-agent chaotic systems with unknown time delays and switching topologies

In this paper the distributed consensus problem for a class of multi-agent chaotic systems with unknown time delays under switching topologies and directed intermittent communications is investigated. Each agent is modeled as a general nonlinear system including many chaotic systems with or without time delays. Based on the Lyapunov stability theory and graph theory, some sufficient conditions guarantee the exponential convergence. A graph-dependent Lyapunov proof provides the definite relationship among the bound of unknown time delays, the admissible communication rate and each possible topology duration. Moreover, the relationship reveals that these parameters have impacts on both the convergence speed and control cost. The case with leader-following communication graph is also addressed. Finally, simulation results verify the effectiveness of the proposed method.     

Transversal Heteroclinic Bifurcation in Hybrid Systems with Application to Linked Rocking Blocks

In this paper, we study heteroclinic bifurcation and the appearance of chaos in time-perturbed piecewise smooth hybrid systems with discontinuities on finitely many switching manifolds. The unperturbed system has a heteroclinic orbit connecting hyperbolic saddles of the unperturbed system that crosses every switching manifold transversally, possibly multiple times. By applying a functional analytical method, we obtain a set of Melnikov functions whose zeros correspond to the occurrence of chaos of the system. As an application, we present an example of quasiperiodically excited piecewise smooth system with impacts formed by two linked rocking blocks.     

Impacts of inventory shortage policies on transportation requirements in two-stage distribution systems

This paper investigates the impacts inventory shortage policies have on transportation costs in base-stock distribution systems under uncertain demand. The model proposed demonstrates how backlogging arrangements can serve to decrease the variability of transportation capacity requirements, and hence the magnitude of transportation costs, when compared with policies that expedite demand shortages. The model shows how inventory policy decisions directly impact expected transportation costs and provides a new method for setting stock levels that jointly minimizes inventory and transportation costs. The model and solution method provide insights into the relationship between inventory decisions and transportation costs and can serve to support delivery policy negotiations between a supplier and customer that must choose between expediting and backlogging demand shortages.     

Optimizing VVT strategies: a decomposition approach

Verification, validation and testing (VVT) of large systems is an important but complex process. The decisions involved have to consider on one hand the controllable variables associated with investments in appraisal and prevention activities and on the other hand the outcomes of these decisions that are associated with risk impacts and systems' failures. Typically, quantitative models of such large systems use simulation to generate distributions of possible costs and risk outcomes. Here, by assuming independence of risk impacts, we decompose the decision process into separate decisions for each VVT activity and supercede the simulation technique by simple analytical models. We explore various optimization objectives of VVT strategies such as minimum total expected cost, minimum uncertainty as well as a generalized optimization objective expressing Taguchi's expected loss function and provide explicit solutions. A numerical example based on simplified data of a case study is used to demonstrate the proposed VVT optimization procedure.     

Controlling the bullwhip effect in a supply chain system with constrained information flows

The bullwhip effect problem is one of the most important issues in supply chain management. Limited information sharing increases the difficulty of reducing the bullwhip effect and leads to inefficient supply chain management. The purpose of this paper is to explore new ways to reduce the bullwhip effect in supply chain systems that face uncertainties with respect to information sharing. We first present a supply chain state transition model, based on which we explore the endogenous mechanism of bullwhip effect, especially those related to impacts from limited information sharing. Then we propose a novel inventory control method and study the corresponding control optimization problem, with the aim of reducing inventory volatility in supply chains. Both quantitative analysis and simulation study are conducted. Simulation results show the effectiveness and flexibility of our proposed method in reducing bullwhip effect and in improving supply chain performance, even under conditions of limited information sharing.     

碰振系统中的共存周期轨道

提出一种寻找分段线性碰振系统中的多个周期轨道共存的分析方法,这些单碰周期轨道包含稳定的和不稳定的轨道。给出了单碰周期轨道存在性或不存在性的解析判别式,特别是对如何保证在单碰周期运动中不会发生其它的碰撞的问题作了比较深入的研究,得到若干定理。最后讨论了所得共存周期轨道的稳定性问题,获得了稳定性的判别式。还以数值模拟结果验证了理论分析的结论。     

Bifurcation sequences of vibroimpact systems near a 1:2 strong resonance point

Two vibroimpact systems are considered, which can exhibit symmetrical double-impact periodic motions under suitable system parameter conditions. Dynamics of such systems are studied by use of maps derived from the equations of motion, between impacts, supplemented by transition conditions at the instants of impacts. Two-parameter bifurcations of fixed points in the vibroimpact systems, associated with 1:2 strong resonance, are analyzed. Interesting features like Neimark–Sacker bifurcation of period-1 double-impact symmetrical motion, tangent bifurcation of period-2 four-impact motion, period-doubling bifurcation of period-2 four-impact motion and Neimark–Sacker bifurcation of period-4 eight-impact motion, etc., are found to occur near 1:2 resonance point of a vibroimpact system. The quasi-periodic attractor, associated with the fixed point of period-1 double-impact symmetrical motion, is destroyed as a tangent bifurcation of fixed points of period-2 four-impact motion occurs. However, for the other vibroimpact system the quasi-periodic attractor is restored via the collision of stable and unstable fixed points of period-2 four-impact motion. The results mean that there exist possibly more complicated bifurcation sequences of period-two cycle near 1:2 resonance points of non-linear dynamical systems.     

Global dynamics of multi‐group dengue disease model with latency distributions

In this paper, by incorporating latencies for both human beings and female mosquitoes to the mosquito‐borne diseases model, we investigate a class of multi‐group dengue disease model and study the impacts of heterogeneity and latencies on the spread of infectious disease. Dynamical properties of the multi‐group model with distributed delays are established. The results showthat the global asymptotic stability of the disease‐free equilibrium and the endemic equilibrium depends only on the basic reproduction number. Our proofs for global stability of equilibria use the classical method of Lyapunov functions and the graph‐theoretic approach for large‐scale delay systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Power-of-two sampling in redundancy systems: The impact of assignment constraints

A classical sampling strategy for load balancing policies is power-of-two, where any server pair is sampled with equal probability. This does not cover practical settings with assignment constraints which force non-uniform sampling. While intuition suggests that non-uniform sampling adversely impacts performance, this was only supported through simulations, and rigorous statements have remained elusive. Building on product-form distributions for redundancy systems, we prove the stochastic dominance of uniform sampling for a four-server system as well as arbitrary-size systems in light traffic.     

Hybrid dynamical systems with controlled discrete transitions

This invited survey focuses on a new class of systems–hybrid dynamical systems with controlled discrete transitions. A type of system behavior referred to as the controlled infinitesimal dynamics is shown to arise in systems with widely divergent dynamic structures and application domains. This type of behavior is demonstrated to give rise to a new dynamic mode in hybrid system evolution–a controlled discrete transition. Conceptual and analytical frameworks for modeling of and controller synthesis for such transitions are detailed for two systems classes: one requiring bumpless switching among controllers with different properties, and the other–exhibiting single controlled impacts and controlled impact sequences under collision with constraints. The machinery developed for the latter systems is also shown to be capable of analysing the behavior of difficult to model systems characterized by accumulation points, or Zeno-type behavior, and unique system motion extensions beyond them in the form of sliding modes along the constraint boundary. The examples considered demonstrate that dynamical systems with controlled discrete transitions constitute a general class of hybrid systems.     

Connectivity modeling and optimization of linear consecutively connected systems with repairable connecting elements

Linear consecutively connected systems (LCCSs) are systems containing a linear sequence of ordered nodes. Connection elements (CE) characterized by diverse connection ranges, time-to-failure and time-to-repair distributions are allocated to different nodes to provide the system connectivity, i.e., a connection between the source and sink nodes of the LCCS. Examples of LCCSs abound in practical applications such as flow transmission systems and radio communication systems. Considerable research efforts have been expended in modeling and optimizing LCCSs. However, most of the existing works have assumed that CEs either are non-repairable or undergo a restrictive minimal repair policy with constant repair time. This paper makes new technical contributions by modeling and optimizing LCCSs with CEs under corrective maintenance with random repair time and different repair policies (minimal, perfect, and imperfect). The characteristics of CEs can depend on their location because the distance between adjacent nodes and conditions of CE operation and maintenance at different nodes can be different, which further complicates the problem. We first propose a discrete numerical algorithm to evaluate the instantaneous availability of each CE. A universal generating function based method is then implemented for assessing instantaneous and expected system connectivity for a specific CE allocation. As the CE allocation can have significant impacts on the system connectivity, we further define and solve the optimal CE allocation problem, whose objective is to find the CE allocation among LCCS nodes maximizing the expected system connectivity over a given mission time. Effects of different parameters including repair efficiency, mission time and repair time are investigated. As illustrated through examples, optimization results can facilitate optimal decisions on robust design and effective operation and maintenance managements of LCCSs.     

A cognitive analytics management framework to select input and output variables for data envelopment analysis modeling of performance efficiency of banks using random forest and entropy of information

The efficiency of banks has a critical role in development of sound financial systems of countries. Data Envelopment Analysis (DEA) has witnessed an increase in popularity for modeling the performance efficiency of banks. Such efficiency depends on the appropriate selection of input and output variables. In literature, no agreement exists on the selection of relevant variables. The disagreement has been an on-going debate among academic experts, and no diagnostic tools exist to identify variable misspecifications. A cognitive analytics management framework is proposed using three processes to address misspecifications. The cognitive process conducts an extensive review to identify the most common set of variables. The analytics process integrates a random forest method; a simulation method with a DEA measurement feedback; and Shannon Entropy to select the best DEA model and its relevant variables. Finally, a management process discusses the managerial insights to manage performance and impacts. A sample of data is collected on 303 top-world banks for the periods 2013 to 2015 from 49 countries. The experimental simulation results identified the best DEA model along with its associated variables, and addressed the misclassification of the total deposits. The paper concludes with the limitations and future research directions.

     

Grazing bifurcation and chaotic oscillations of vibro-impact systems with one degree of freedom

The bifurcations of dynamical systems, described by a second-order differential equation with periodic coefficients and an impact condition, are investigated. It is shown that a continuous change in the coefficients of the system, during which the number of impacts of the periodic solution increases, leads to the occurrence of a chaotic invariant set.     

On the adiabatic perturbation theory for systems with impacts

A basis for the applicability of the formal scheme of adiabatic perturbation theory for systems with impacts is given using the example of three well-known problems, namely, a small sphere between slowly moving walls, rays in a smoothly irregular waveguide with reflecting walls, and an adiabatic piston.     

How to benefit from decision analysis in environmental life cycle assessment (LCA)

Environmental life cycle assessment (LCA) is one method to support environmental information needs by multi-attribute product evaluations. LCA describes the environmental effects associated with a product, process or activity over its whole life cycle by calculating the material and energy requirements as well as emissions to air, water and soil and by assessing the environmental impacts of those. An LCA study has both objective and subjective steps. So far, LCA has been developed without much consideration of the literature on decision modelling. We want to show that approaches and tools from decision analysis would be beneficial both in the planning of an LCA study and in the interpretation and understanding of the results. We describe the LCA methodology and application, and discuss how the integration of decision analysis and LCA could improve LCA as a tool for decision making. We use an LCA study on beverage packaging systems to illustrate the new approach.     

双侧弹性约束悬臂梁的非光滑擦边动力学北大核心CSCD

研究了具有双侧弹性约束的单自由度悬臂梁系统擦边诱导的非光滑动力学行为.首先,基于弹性碰撞悬臂梁的动力学方程和擦边点的定义,分析了双侧擦边周期运动的存在性条件.其次,选取零速度的Poincaré截面,推导了双侧擦边轨道附近带参数的高阶不连续映射.然后,结合光滑流映射和高阶不连续映射建立了新的复合分段范式映射.最后,将基于低阶范式映射和高阶范式映射得到的分岔图进行对比,分析验证了高阶范式映射的有效性,并通过数值仿真进一步揭示了弹性碰撞悬臂梁的擦边动力学.     

MOIRA: A decision support system for decision making on aquatic ecosystems contaminated by radioactive fallout

Interventions to restore radionuclide contaminated aquatic ecosystems may reduce individual and collective radiation doses, but may also result in detrimental ecological, social and economic effects. Decision makers must carefully evaluate possible impacts before choosing a countermeasure, hence decision analysis methods constitute an important aid to rank intervention strategies after the contamination of an aquatic ecosystem. We describe MOIRA, a decision support system for the identification of optimal remedial strategies to restore water systems after accidental introduction of radioactive substances. MOIRA includes an evaluation module based on a multi-attribute value model to rank alternatives and a module to perform multiparametric sensitivity analyses, both with respect to weights and values, to allow us to gain insights into the problem. The problem is under certainty since the validation of models used to quantify countermeasure impacts suggests little uncertainty in policy effects.The system is implemented in a PC based decision support system which allows the inclusion of all relevant information.     

The stability of equilibrium in systems with friction

Mechanical systems with non-ideal geometrical constraints are considered. The possible lack of uniqueness of the solution of the problem of determining the generalized accelerations and reactions with respect to specified coordinates and velocities is taken into account in solving the problem of the stability of an equilibrium state. A number of necessary and sufficient conditions of stability are obtained. It is shown that the results are also applicable in the case of unilateral constraints subject to the condition that a specific hypothesis concerning the character of the impacts on the constraints is adopted. A problem on the stability of a rigid body on a rough plane in the two-dimensional case is solved as an example.