Behavior Data Analysis of English Learners Based on Discrete Dynamic System Modeling Method.

The traditional models of distributed computing systems employ the mathematical formalisms of discrete event dynamical systems along with Petri Nets. However, such models are complex to analyze and computationally expensive. Interestingly, the evolving distributed computing systems closely resemble the discrete dynamical systems. This paper constructs and analyzes the model of distributed computing systems by applying mathematical formalisms of the discrete dynamical systems. The proposed model embeds the partial ordering of states under happened-before relation in the set of globally observable states. The stability of the proposed model is analyzed using the first order linear approximation.

A Petri net with controller is used to model discrete events in flexible job shop scheduling, the objective of scheduling problems is to minimize make-span, the scheduling results is obtained based on genetic and Tabu Search (TS) algorithm. It is proved capable of providing optimized schedule to the job-shop where the machine tool and manpower resources are both constrained. After crossover and mutation operations, an optimal or suboptimal scheduling plan can be found. The result of the test shows that this method is feasible and efficient. Job shop scheduling is the primary content and critical technology of the production management of CIMS, in the past during 30 years, a lot of researchers and results focus on it, but most of them deal with single objective and resource scheduling problems which are fixed processing route and constrained by machine, and production period is its optimal objective. Nevertheless, the production styles are variable and processing route is determined under the special condition. Moreover, job shop scheduling problem is the most difficult combined constraints optimal problem and typical NP hard problem which can't be solved in polynomial time by an effective algorithm. Up to date, there are some traditional algorithms to solve JSP problem (1-2). About paper (3), Petri net is used to construct JSP model and L1 which combines branch and bound algorithm with dynamic program is used to search its optimal solution. And paper (4), the job sequence is assigned by genetic code firstly, and then filtered beam search which based on breadth-first algorithm is adopted to search. In recent years, the Petri net as a discrete event dynamic system modeling and analysis tool(5), has been successfully applied to the flexible manufacturing system modeling, analysis and control. Some researchers put forward to be based on Petri network scheduling method, but only on the production line itself can not reflect the modeling, as in the production line of external control scheduling strategy influence. A hybrid algorithm is proposed to solve dual-resource scheduling problem in flexible production environment, and Petri net model with a controller, which can effectively model control. It combines the advantage of global search ability of GA with the self-adaptive merit of Tabu Search (TS) and improves its convergence. It is proved capable of global and part searching ability and efficient.

Biological neurons are typically modeled using the Hodgkin-Huxley formalism, which requires significant computational power to simulate. However, since realistic neural network models require thousands of synaptically coupled neurons, a faster approach is needed. Discrete dynamical systems are promising alternatives to continuous models, as they can simulate neuron activity in far fewer steps. Many existing discrete models are based on Poincaré-map-like approaches, which trace periodic activity at a cross section of the cycle. However, this approach is limited to periodic solutions. Biological neurons have many key properties beyond periodicity, such as the minimum applied current required for a resting cell to generate an action potential. To address these properties, we propose a discrete dynamical system model of a biological neuron that incorporates the threshold dynamics of the Hodgkin-Huxley model, the logarithmic relationship between applied current and frequency, modifications to relaxation oscillators, and spike-frequency adaptation in response to modulatory hyperpolarizing currents. It is important to note that several critical parameters are transferred from the continuous model to our proposed discrete dynamical system. These parameters include the membrane capacitance, leak conductance, and maximum conductance values for sodium and potassium ion channels, which are essential for accurately simulating the behavior of biological neurons. By incorporating these parameters into our model, we can ensure that it closely approximates the continuous model’s behavior, while also offering a more computationally efficient alternative for simulating neural networks.

Consider a discrete dynamical system given by a square matrix $M \in \mathbb{Q}^{d \times d}$ and a starting point $s \in \mathbb{Q}^d$. The orbit of such a system is the infinite trajectory $\langle s, Ms, M^2s, \ldots\rangle$. Given a collection $T_1, T_2, \ldots, T_m \subseteq \mathbb{R}^d$ of semialgebraic sets, we can associate with each $T_i$ an atomic proposition $P_i$ which evaluates to true at time $n$ if, and only if, $M^ns \in T_i$. This gives rise to the LTL Model-Checking Problem for discrete linear dynamical systems: given such a system $(M,s)$ and an LTL formula over such atomic propositions, determine whether the orbit satisfies the formula. The main contribution of the present paper is to show that the LTL Model-Checking Problem for discrete linear dynamical systems is decidable in dimension 3 or less.

This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams. After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.

We describe the destabilizing (in the sense of a decrease in the reserve of mean-square asymptotic stability) effect of random parametric perturbations of the white-noise type in quasilinear continuous and discrete dynamical systems (Lur’e-Postnikov systems of automatic control with nonlinear feedback). We use stochastic Lyapunov functions in the form of linear combinations of the types “a quadratic form of phase coordinates plus the integral of a nonlinearity” (continuous systems) and “a quadratic form of phase coordinates plus the integral sum for a nonlinearity” (discrete systems) and the matrix algebraic Sylvester equations associated with stochastic Lyapunov functions of this form.

The core of fault diagnosis expert system is diagnostic knowledge representation and reasoning. Fuzzy Petri nets (FPN) have been testified to an ideal tool for knowledge representation and reasoning. However, when using FPN for diagnostic knowledge representation and reasoning, fault symptoms will disappear after fault propagated. This is not congruous with factual fault propagation. Another major limitation is the lacking of formal reasoning algorithm of FPN, which leads to it can't be implemented expediently by computer. In view of the limitations of FPN based diagnostic knowledge representation and reasoning, an enhanced model named fuzzy fault Petri nets (FFPN) and its formal reasoning algorithm are presented in the paper. A fault diagnosis instance was used to verify the feasibility and validity of the proposed method. It is demonstrated that this method is quite effective.

On the fluidization of Petri nets and marking homothecy

A new Petri net modeling technique for the performance analysis of discrete event dynamic systems

This paper presents a decentralized Petri net (PN) based wireless sensor node architecture (PN-WSNA) to construct a flexible and reconfigurable WSN for intelligent monitoring systems. PN is a graphic based discrete event dynamic system (DEDS) modeling approach, and it is advantageous for modeling the system with concurrent and asynchronous systems. Therefore, the PN is usually used to construct agent based intelligent monitoring systems. The PN-WSNA system consists of a PN-WSNA kernel program and a PN-WSNA management program. The PN-WSNA kernel program is developed as an agent that is installed in the sensor node, and it is responsible of receiving and decoding PN models, collecting sensor data from analog and digital channels, intercommunication between sensor nodes, PN model inference and decision. On the other hand, the PN-WSNA management program is executed on a remote host computer, and it is responsible of distance sensor node managements via routing tables. More specially, a user interface is provided for system managers to edit PN models in a graphic manner, and the PN models can be delivered to the corresponding sensor node online without physical visits. Therefore, the proposed PN-WSNA system not only performs a reconfigurable WSN architecture, but also provides an easy graphical PN edit environment for constructing intelligent agents. Such a system can be applied to the factory automation, intelligent diagnosis, climate monitoring, etc. Finally, a simple prototype system is constructed using the Zigbee BAT mote modules to verify the proposed PN-WSNA system.

The costs and benefits of introducing auto-identification are difficult to evaluate. The Return On Investment (ROI) may be calculated on manufacturing environments but in some service providing systems, like hospitals, it may be very hard and inaccurate to judge the relevance of a new configuration only through financial considerations. New information and communication technologies and devices appear rapidly. This study aims at quantifying the benefits of introducing new devices at different levels in a complex socio-technical system: a biobank (storage, transformation and exchanges of biological samples) using a discrete event dynamic systems simulation model as a quality measurement tool. After introducing the context, we will describe pertinent measurement possibilities adapted to the Supply Chain for Health services, and particularly to biobanks, and the way we implemented the simulation model used to get the results summarized in the last section, before concluding. The originalities of this paper are the process modeling, designed to be easily modified to test many different configurations and scenarios, and the quality indicators that are particularly adapted to health services.

This work is about examples of applications of group classifications for continuous (differential equations) and discrete models of flow in porous media. Difference schemes and discrete dynamical systems are considered as discrete models. Group classifications has been carried out on the basis of continuous groups (Lie groups) of transformations in n-dimensional Euclidean spaces. The example of explicit difference scheme for Buckley-Leverett equation has been demonstrated where the correspondence to one of classes of the obtained earlier classifications of discrete dynamical system has been shown. The example of fractal capillary network on the basis of Sierpinski triangle has been demonstrated for the group classification of discrete dynamical systems. The approach of continuous symmetry absence or presence proof has been demonstrated using classifications of discrete dynamical systems. Difference schemes with continuous symmetry groups for partial differential equations of parabolic type, which correspond to the equation of gas flow in porous media and Rapoport-Leas equation (generalized Buckley-Leverett equation), are considered. Examples of difference schemes for these cases are given and related to classes of the obtained earlier classifications. Applications of continuous symmetry groups for numerical solutions generations are demonstrated for these cases.

Discrete event dynamic systems (DEDS), are systems, which change state over time, based on current state and state transition rules. Each state is separated from its neighbour by a step rather than a continuum of infinitesimal states. This continuum in DEDS needs a representation between 0 and 1. The application of fuzzy logic in defining and modelling the DEDS is suggested as a possible solution because the nature of DEDS may be asynchronous, distributed, parallel, non-deterministic and/or stochastic. This results in the generalisation of crisp finite automata into fuzzy automata for a DEDS. In this paper, a DEDS in the form of hopper feed system is considered. The system is reformulated using state vectors and event transition matrices and is extended to fuzzy vectors and matrices. An algorithm is proposed for the final control action to be implemented using a programmable logic controller (PLC).

systems. In this paper, we firstly study the Noether symmetry and Noether exact invariants of discrete nonconservative dynamical systems. Secondly, we study perturbation to symmetry and adiabatic invariants of discrete dynamical systems. Finally, we give an example to illustrate the application of these results.

This paper focuses on discrete dynamic optimization on train rescheduling on single-track railway with the consideration of train punctuality and station satisfaction degree. A discrete dynamic system is firstly described to mimic train rescheduling, and a state transition function is specially designed according to the train departure event. The purpose of this function is to improve simulation efficiency by directly confirming the next discrete time. After the construction and analysis of optimization models to discrete dynamic system, a two-stage heuristic search strategy is developed, by using clustering hierarchy theory and stochastic search strategy, to obtain train departure time and arrival time before each state transition of the system. Finally, a numerical experiment is conducted to verify the proposed system, models, and the heuristic search strategy. The result shows that the discrete dynamic system, together with the state transition function and heuristic search strategy, shows better performance in simulation efficiency and solution quality.