Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.

Research on the self-defence electronic jamming decision-making based on the discrete dynamic Bayesian network

The manner and conditions of running the decision-making system with self-defense electronic jamming are given. After proposing the scenario of applying discrete dynamic Bayesian network to the decision making with self-defense electronic jamming, a decision-making model with self-defense electronic jamming based on the discrete dynamic Bayesian network is established. Then jamming decision inferences by the aid of the algorithm of discrete dynamic Bayesian network are carried on. The simulating result shows that this method is able to synthesize different targets which are not predominant. In this way, various features at the same time, as well as the same feature appearing at different time complement mutually; in addition, the accuracy and reliability of electronic jamming decision making are enhanced significantly.

CYCLIC HARDENING BEHAVIOR OF POLYCRYSTALS WITH PENETRABLE GRAIN BOUNDARIES:TWO-DIMENSIONAL DISCRETE DISLOCATION DYNAMICS SIMULATION

A two-dimensional discrete dislocation dynamics （DDD） technology by Giessen and Needleman （1995）, which has been extended by integrating a dislocation-grain boundary interaction model, is used to computationally analyze the micro-cyclic plastic response of polycrystals containing micron-sized grains, with special attentions to significant influence of dislocationpenetrable grain boundaries （GBs） on the micro-plastic cyclic responses of polycrystals and underlying dislocation mechanism. Toward this end, a typical polycrystalline rectangular specimen under simple tension-compression loading is considered. Results show that, with the increase of cycle accumulative strain, continual dislocation accumulation and enhanced dislocation-dislocation interactions induce the cyclic hardening behavior; however, when a dynamic balance among dislocation nucleation, penetration through GB and dislocation annihilation is approximately established, cyclic stress gradually tends to saturate. In addition, other factors, including the grain size, cyclic strain amplitude and its history, also have considerable influences on the cyclic hardening and saturation.

Target threat estimation based on discrete dynamic Bayesian networks with small samples

The accuracy of target threat estimation has a great impact on command decision-making.The Bayesian network,as an effective way to deal with the problem of uncertainty,can be used to track the change of the target threat level.Unfortunately,the traditional discrete dynamic Bayesian network(DDBN)has the problems of poor parameter learning and poor reasoning accuracy in a small sample environment with partial prior information missing.Considering the finiteness and discreteness of DDBN parameters,a fuzzy k-nearest neighbor(KNN)algorithm based on correlation of feature quantities(CF-FKNN)is proposed for DDBN parameter learning.Firstly,the correlation between feature quantities is calculated,and then the KNN algorithm with fuzzy weight is introduced to fill the missing data.On this basis,a reasonable DDBN structure is constructed by using expert experience to complete DDBN parameter learning and reasoning.Simulation results show that the CF-FKNN algorithm can accurately fill in the data when the samples are seriously missing,and improve the effect of DDBN parameter learning in the case of serious sample missing.With the proposed method,the final target threat assessment results are reasonable,which meets the needs of engineering applications.

Experiments of Reconstructing Discrete Atmospheric Dynamic Models from Data (I)

In this paper, we give some experimental results of our study in reconstructing discrete atmospheric dynamic models from data. After a great deal of numerical experiments, we found that the logistic map, xn +1= 1-uxn2 could be used in monthly mean temperature prediction when it was approaching the chaotic region, and its predictive results were in reverse states to the practical data. This means that the nonlinear developing behavior of the monthly mean temperature system is bifurcating back into the critical chaotic states from the chaotic ones.

THE DISCRETE DYNAMICS FOR COMPETITIVE POPULATIONS OF LOTKA-VOLTERRA TYPE

The discrete dynamics for competition populations of Lotka-Volterra type modeled as N1(t+1)=N1(t) exp[r1(1-N1-b12N2)], N2(t+1)=N2(t) exp[r2(1-N2-b21N1)] is considered in the paper. In the case of non-persistence the attractive behavior of model has been discussed. Especially, there are two attractive sets when h_(ij)>1, and the attractive behaviors are more complicated than that of the corresponding cofitinuous model. The attracted regions are given. We prove that the model is also persistent in the degenerate case of b_(ij)=1. In the persistence case of b_(ij)<1, the existence and uniqueness for two-period points of the model are studied at r1=r2. The condition for the multi-pair of two-period points is indicated and their influences on population dynamical behaviors are shown.

Robust impulsive synchronization of linear discrete dynamical networks

This paper aims to study robust impulsive synchronization problem foruncertain linear discrete dynamical network. For the discrete dynamical networks with unknown butbounded linear coupling, by introducing the concept of uniformly positive definite matrix functions,some robust impulsive controllers are designed, which ensure that the state of a discrete dynamicalnetwork globally asymptotically synchronizes with an arbitrarily assigned state of an isolate nodeof the network. This paper also investigates the synchronization problem where the network couplingfunctions are uncertain but bounded nonlinear functions. Finally, two examples are simulated toillustrate our results.

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”.

Behaviours in a dynamical model of traffic assignment with elastic demand

This paper investigates the dynamical behaviour of network traffic flow. Assume that trip rates may be influenced by the level of service on the network and travellers are willing to take a faster route. A discrete dynamical model for the day-to-day adjustment process of route choice is presented. The model is then applied to a simple network for analysing the day-to-day behaviours of network flow. It finds that equilibrium is arrived if network flow consists of travellers not very sensitive to the differences of travel cost. Oscillations and chaos of network traffic flow are also found when travellers are sensitive to the travel cost and travel demand in a simple network.

MODELING AND PERFORMANCE ANALYSIS FOR THE SERIAL AND PARALLEL PRODUCTION SYSTEM BASED ON GSPN

Differed from the existed applications of generalized stochastic Petri net(GSPN) theory in machine-tool manufacturing system, reliability computation of FMS, testabilityparameters determination and fault analysis, a new idea of applying GSPN to model and performanceanalysis for the serial and parallel production system is proposed. And one typical discrete eventdynamic system (DEDS), turner-unit of palletizing system, is taken as a real case to research. Basedupon the established GSPN models, the working performances of serial and parallel layout arecompared. Furthermore, their differences of working mechanisms including feeding mechanism,coordinating mechanism and monitoring mechanism are discussed. Thus the theoretical basis which ishelpful to appraise layout plan and its reasonableness is provided. Meanwhile, the research resultsshow that parallel layout is more advantageous to greatly improve the operational speed ofproduction system than serial one.

Discrete Conley index and bifurcation points

In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.

Micropillar compression using discrete dislocation dynamics and machine learning

Discrete dislocation dynamics(DDD)simulations reveal the evolution of dislocation structures and the interaction of dislocations.This study investigated the compression behavior of single-crystal copper micropillars using fewshot machine learning with data provided by DDD simulations.Two types of features are considered:external features comprising specimen size and loading orientation and internal features involving dislocation source length,Schmid factor,the orientation of the most easily activated dislocations and their distance from the free boundary.The yielding stress and stress-strain curves of single-crystal copper micropillar are predicted well by incorporating both external and internal features of the sample as separate or combined inputs.It is found that the machine learning accuracy predictions for single-crystal micropillar compression can be improved by incorporating easily activated dislocation features with external features.However,the effect of easily activated dislocation on yielding is less important compared to the effects of specimen size and Schmid factor which includes information of orientation but becomes more evident in small-sized micropillars.Overall,incorporating internal features,especially the information of most easily activated dislocations,improves predictive capabilities across diverse sample sizes and orientations.

Dynamics of a Bertrand Duopoly Game of the Greek Oil Market and Application of the d-Backtest Method

This work presents the complexity that emerges in a Bertrand duopoly between two companies in the Greek oil market, one of which is semi-public and the other is private. The game uses linear demand functions for differentiated products from the existing literature and asymmetric cost functions that arose after approaches using the published financial reports of the two oil companies (Hellenic Petroleum and Motor Oil). The game is based on the assumption of homogeneous players who are characterized by bounded rationality and follow an adjustment mechanism. The players’ decisions for each time period are expressed by two difference equations. A dynamical analysis of the game’s discrete dynamical system is made by finding the equilibrium positions and studying their stability. Numerical simulations include bifurcation diagrams and strange attractors. Lyapunov numbers’ graphs and sensitivity analysis in initial conditions prove the algebraic results and reveal the complexity and chaotic behavior of the system focusing on the two parameters k1 and k2 (speed of adjustment for each player). The d-Backtest method is applied through which an attempt is made to control the chaos that appears outside the stability space in order to return to the locally asymptotically stable Nash equilibrium for the system.

Modeling and Stability Analysis of a Communication Network System

In this work, the modeling and stability problem for a communication network system is addressed. The communication network system consists of a transmitter which sends messages to a receiver. The proposed model considers two possibilities. The first one, that messages are successfully received, while in the second one, during the sending process the transmitter breaks down and as a result the message does not reach the receiver. Timed Petrinets is the mathematical and graphical modeling technique utilized. Lyapunov stability theory provides the required tools needed to aboard the stability problem. Employing Lyapunov methods, a sufficient condition for stabilization is obtained. It is shown that it is possible to restrict the communication network system state space in such a way that boundedness is guaranteed. However, this restriction results to be vague. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.

Recognition Methods of Geometrical Images of Automata Models of Systems in Control Problem

The laws of functioning of discrete deterministic dynamical systems are investigated,presented in the form of automata models defined by geometric images.Due to the use of the apparatus of geometric images of automata,developed by V.A.Tverdokhlebov,the analysis of automata models is carried out on the basis of the analysis of mathematical structures represented by geometric curves and numerical sequences.The purpose of present research is to further develop the mathematical apparatus of geometric images of automaton models of systems,including the development of new methods for recognizing automata by their geometric images,given both geometric curves and numerical sequences.

The excluded-volume effect in microscopic pedestrian simulations

We propose a pedestrian position update rule, which is added to a microscopic pedestrian model to avoid pedestrian overlap. In the rule, the step size of a pedestrian moving in a selected direction at each update is in inverse proportion to the repulsive actions imposed by other pedestrians moving in a direction with an exponential rate. The positions of the pedestrians are then updated in each small time interval. In this way, a barrier between the pedestrians can be generated, and after updating their positions the pedestrians do not overlap with each other. The modified model is compared to the original model through a simulation of the evacuation process of pedestrians in a closed area. The simulation results indicate that the modified model is superior to the original model in several aspects.

The Bistability Theorem in a Model of Metastatic Cancer

The main theorem of the present paper is the bistability theorem for a four dimensional cancer model, in the variables representing primary cancer C, metastatic cancer , growth factor GF and growth inhibitor GI, respectively. It says that for some values of the para- meters this system is bistable, in the sense that there are exactly two positive singular points of this vector field. And one is stable and the other unstable. We also find an expression for for the discrete model T of the introduction, with variables , where C is cancer, are growth factors and growth inhibitors respectively. We find an affine vector field Y whose time one map is T2 and then compute , where is an integral curve of Y through . We also find a formula for the first escape time for the vector field associated to T, see section four.

A combined multiscale modeling and experimental study on surface modification of high-volume micro-nanoparticles with atomic accuracy

Surface modification for micro-nanoparticles at the atomic and close-to-atomic scales is of great importance to enhance their performance in various applications,including high-volume battery,persistent luminescence,etc.Fluidized bed atomic layer deposition(FB-ALD)is a promising atomic-scale manufacturing technology that offers ultrathin films on large amounts of particulate materials.Nevertheless,nanoparticles tend to agglomerate due to the strong cohesive forces,which is much unfavorable to the film conformality and also hinders their real applications.In this paper,the particle fluidization process in an ultrasonic vibration-assisted FB-ALD reactor is numerically investigated from micro-scale to macro-scale through the multiscale computational fluid dynamics and discrete element method(CFD-DEM)modeling with experimental verification.Various vibration amplitudes and frequencies are investigated in terms of their effects on the fluid dynamics,distribution of particle velocity and solid volume fraction,as well as the size of agglomerates.Results show that the fluid turbulent kinetic energy,which is the key power source for the particles to obtain the kinetic energy for overcoming the interparticle agglomeration forces,can be strengthened obviously by the ultrasonic vibration.Besides,the application of ultrasonic vibration is found to reduce the mean agglomerate size in the FB.This is bound to facilitate the heat transfer and precursor diffusion in the entire FB-ALD reactor and the agglomerates,which can largely shorten the coating time and improve the film conformality as well as precursor utilization.The simulation results also agree well with our battery experimental results,verifying the validity of the multiscale CFD-DEM model.This work has provided momentous guidance to the mass manufacturing of atomic-scale particle coating from lab-scale to industrial applications.

A Novel Dynamic Quadrature Scheme for Solving Boltzmann Equation with Discrete Ordinate and Lattice Boltzmann Methods

The Boltzmann equation(BE)for gas flows is a time-dependent nonlinear differential-integral equation in 6 dimensions.The current simplified practice is to linearize the collision integral in BE by the BGK model using Maxwellian equilibrium distribution and to approximate the moment integrals by the discrete ordinatemethod(DOM)using a finite set of velocity quadrature points.Such simplification reduces the dimensions from 6 to 3,and leads to a set of linearized discrete BEs.The main difficulty of the currently used(conventional)numerical procedures occurs when the mean velocity and the variation of temperature are large that requires an extremely large number of quadrature points.In this paper,a novel dynamic scheme that requires only a small number of quadrature points is proposed.This is achieved by a velocity-coordinate transformation consisting of Galilean translation and thermal normalization so that the transformed velocity space is independent of mean velocity and temperature.This enables the efficient implementation of Gaussian-Hermite quadrature.The velocity quadrature points in the new velocity space are fixed while the correspondent quadrature points in the physical space change from time to time and from position to position.By this dynamic nature in the physical space,this new quadrature scheme is termed as the dynamic quadrature scheme(DQS).The DQS was implemented to the DOM and the lattice Boltzmann method(LBM).These new methods with DQS are therefore termed as the dynamic discrete ordinate method(DDOM)and the dynamic lattice Boltzmann method(DLBM),respectively.The new DDOM and DLBMhave been tested and validated with several testing problems.Of the same accuracy in numerical results,the proposed schemes are much faster than the conventional schemes.Furthermore,the new DLBM have effectively removed the incompressible and isothermal restrictions encountered by the conventional LBM.