Complex Dynamic Theory Research Articles

Attitudes, Motivation, and Beliefs of Online Foreign Language Learners Amidst the Pandemic

Covid-19 pandemic was an event which undeniably changed the paradigm of language learning. Online language learning has emerged as a significant catalyst, shedding light on distinctive attitudes, motivations, and beliefs among learners. The aim of the present study was to explore how learners articulated their attitudes, motivations, and beliefs in this context. To achieve these objectives, two hundred thirteen respondents participated in the study, completing modified versions of the AMTB (Attitude/Motivation Test Battery) and BALLI (Beliefs about Language Learning Inventory) questionnaires. In addition, eight online language learners were engaged in one-on-one interviews. Quantitative data were subjected to descriptive statistical analysis, while qualitative data were transcribed and examined using thematic analysis techniques as proposed by Auerbach & Silverstein (2003). Drawing upon the Complex Dynamic Theory by Larsen-Freeman (2017), the study's findings revealed that foreign language learning during the Covid-19 pandemic constitutes a complex dynamic construct that is profoundly influenced by learners' attitudes, motivations, and beliefs. These findings align with prior research, suggesting that learners generally have positive attitudes toward language learning and the target language community, and they exhibit a high level of motivation in their pursuit of online language acquisition.

Teacher’s Self-concept Change from Complex Dynamic Theory during a Practicum

Teacher’s self-concept is developed from inner and it is gradually formed and developed. However, the practicum is an important link between pre-service education and post-service practice. In order to realize the integration of pre-service and post-service education, this study focused on the Complex Dynamic System Theory, which is an important theory to research teacher’s recognition, to analyze how the self-concept is changed during the practicum. “Intervention”, as a core concept of the theory, will influence pre-service teacher’s concepts. This study was expected to be carried out in a middle school in Jiaozuo. A case study was needed in this research for six months and one participant was invited, who had finished the related courses without teaching experience. She was willing to write diaries and loves teaching. 30 diaries and one internship summary of a pre-service teacher were conducted and analyzed by the means of the grounded theory method. Besides, the pre-service teacher was interviewed as a supplement, which could provide the study with more details about the internship. Summing up and recording was also crucial if necessary. According to this study, it is suggested that the pre-service teacher’s self-concept had complex dynamic changes in three aspects of self-concept. Intervention can be triggered by the following: significant persons, critical events, and social relationships.

Oral English Development of EFL Learners from the Perspective of Complexity Dynamic Theory

With the development of economic globalization and cultural integration, the learning of a second language has become increasingly important for economic, political, and cultural exchanges in the world today. Complex dynamic system theory is an important research theory of foreign language learning methods for nonnative speakers. However, the research and application of the complex dynamic system theory in oral foreign language learning of English as a Foreign Language (EFL) learners are not prominent. The purpose of this paper is to explore the learning situation of oral English of EFL learners from the perspective of the complex dynamic system theory and provide some new learning methods and suggestions for EFL learners’ oral English learning based on the research of complex dynamic system theory. First, this article discusses and analyzes the current situation of oral English learning of EFL learners through literature research and a questionnaire survey. Then, based on the related research on the theory of complex dynamic systems, this article proposes countermeasures and learning method recommendations for the problems existing in the current oral English learning of EFL learners. After that, this paper sets up a controlled test of oral English learning through the learning method formulated by the complex dynamic system theory and verifies the learning effect of the oral English learning method proposed in this paper according to the mathematical theory research method of the complex dynamic system. Finally, this article discusses the reliability of the experimental research conclusions based on the error analysis and confidence level estimation of the experimental results. The research results show shows that there is 95% confidence that the second language learning method proposed in this paper under the perspective of the complex dynamic system theory has a positive effect on the oral English learning of EFL learners.

Exploration of the Compilation of English Learning Materials for Chinese College Students Based on Big Data under the Guidance of Complex Dynamic Theory

With the help of big data and Citespace software, this research makes a statistical analysis of the journals and dissertations on College English teaching and learning materials collected by CNKI from 2011 to 2020. This paper, based on the knowledge map drawn by the visualized analysis of literatures volume, authors, research institutions and keywords clustering, analyzes the current research status and hotspots in the compilation of China’s College English textbooks. It is found that there are six problems in the compilation. Because of the complexity of teaching and learning materials and the dynamic progress of language learning, the nature of English teaching and learning materials is bound to turn from a learning tool to learning resources. Thus, this research, from the perspective of Complex Dynamic System Theory, attempts to develop big data-based College English learning materials with digital, individual and multi-dimensional characteristics by three paths: the establishment of big data-based English learning behaviors index system, the development of big data-based College English learning materials and the application of big data-based College English learning materials. This paper will explore a new way of developing China’s College English learning materials, improve and optimize the compilation and development of College English learning materials in China.

TASK BASED LANGUAGE TEACHING TO IMPROVE STUDENTS’ WILLINGNESS TO COMMUNICATE IN ENGLISH CLASS

The changing of English language teaching method from Audio-lingual Method to Communicative Language Teaching (CLT) has given great impact to the pedagogy of teaching English as a Foreign Language (EFL) and/ or English as a Second Language (ESL). Task Based Language Teaching (TBLT) method which emphasizes more on the meaning of a language and targeted tasks, then, dominates the English teaching world as a response to the un-satisfaction towards the previous methods (Long, 2015). This current study aims at seeing to what extent the task variety influences students’ willingness to communicate based on three contexts which include trait-like, situation, and linguistic. Three communicative tasks which emphasizes both on focused meaning and focused form were given. The communicative tasks include game, problem solving, and jigsaw. Observation was done during class interaction and continued with in depth interview. The result shows that emotion, class situation, and cognitive simultaneously influence the students’ willingness to communicate in English class. Those factors are inseparable, interact and influence interchangeably on the students’ willingness to communicate in English class as elucidated in complex dynamic theory.

Dynamical study while searching equilibrium solutions in [formula omitted]-body problem

The theory of complex dynamics is usually applied to compare the global convergence properties of different iterative methods, by obtaining the attraction basins for simple polynomial equations in the complex domain. However, in this work, we use it in quite another context: the study of a nontrivial nonlinear system that describes the motion of interacting bodies in celestial mechanics, namely, Newtonian planar circular restricted four-body problem and its relative equilibrium solutions. These have been investigated from a dynamical point of view. New properties of the solutions of this system have been obtained. Practical guidelines for efficient search of relative equilibrium solutions of N-body problem have been given.

Non-Linear Dynamics and Complexity in Economics: A Historical Overview

In the last years, non-linear dynamics and complexity gained an important role in economics. Non-linear models are the analytical foundation of complex dynamic theory. This class of models is able to capture more conveniently and more naturally economic behaviors that are non-regular, such as financial market dynamics, economic growth, price fluctuations, business cycle, and diffusion processes. Furthermore, from the early 80s, complex dynamics has become progressively a component of the more general theory of complexity initially developed at the Santa Fe Institute. This paper provides an overview of the historical evolution of these new approaches to economics. In particular, we emphasize the role of mathematical tools that have been applied to formalize dynamic problems in economics.

Wandering domains and nontrivial reduction in non-Archimedean dynamics

Let K be a non-archimedean field with residue field k, and suppose that k is not an algebraic extension of a finite field. We prove two results concerning wandering domains of rational functions φ ∈ K(z) and Rivera-Letelier’s notion of nontrivial reduction. First, if φ has nontrivial reduction, then assuming some simple hypotheses, we show that the Fatou set of φ has wandering components by any of the usual definitions of “components of the Fatou set”. Second, we show that if k has characteristic zero and K is discretely valued, then the existence of a wandering domain implies that some iterate has nontrivial reduction in some coordinate. The theory of complex dynamics in dimension one, founded by Fatou and Julia in the early twentieth century, concerns the action of a rational function φ ∈ C(z) on the Riemann sphere P(C) = C∪{∞}. Any such φ induces a natural partition of the sphere into the closed Julia set Jφ, where small errors become arbitrarily large under iteration, and the open Fatou set Fφ = P (C) Jφ. There is also a natural action of φ on the connected components of Fφ, taking a component U to φ(U), which is also a connected component of the Fatou set. In 1985, using quasiconformal methods, Sullivan [32] proved that φ ∈ C(z) has no wandering domains; that is, for each component U of Fφ, there are integers M ≥ 0 and N ≥ 1 such that φ(U) = φ(U). We refer the reader to [1, 13, 24] for background on complex dynamics. Recall that a non-archimedean metric on a space X is a metric d which satisfies the ultrametric triangle inequality d(x, z) ≤ max{d(x, y), d(y, z)} for all x, y, z ∈ X. In the past two decades, beginning with a study of linearization at fixed points by Herman and Yoccoz [19], there have been a number of investigations of non-archimedean dynamics; for a small sampling, see [4, 5, 6, 10, 20, 27, 28, 31]. It is natural to ask which properties of complex dynamics extend to the non-archimedean setting and which do not. We fix the following notation throughout this paper. K a complete non-archimedean field with absolute value | · | K an algebraic closure of K CK the completion of K OK the ring of integers {x ∈ K : |x| ≤ 1} of K k the residue field of K OCK the ring of integers {x ∈ CK : |x| ≤ 1} of CK k the residue field of CK Date: July 30, 2003. 2000 Mathematics Subject Classification. Primary: 11S80; Secondary: 37F10, 54H20.