A dynamic system refers to a system that changes over time according to deterministic evolution, also known as a dynamical system, which comes from classical mechanics. The development of modern control theory promotes the study of dynamic systems and expands its application to systems in the general sense. Like other natural sciences and engineering laws, the dynamic system is mainly used to describe complex and nonlinear dynamic systems, to identify the relationship between the state of the system at some point and future. Currently, the theory has been widely used in many disciplines such as meteorology, mathematics, economics, physics, and oceanography.
Key concepts in DST
Obviously, the key words in DST are âsystemâ and âdynamicâ. A system is usually looked on as a collection of âcomponents that affect and change one another over timeâ (van Geert, 2003, p. 655). The system is made up of the interactions between these components and is âdynamically stable and self-maintainingâ (van Geert, 1993, p. 268). Complex systems such as language are always multi-component and the development of the system is nonlinear. Dynamic systems are âcomplexes of parts or aspects which are all evolving in a continuous, simultaneous, and mutually determining fashionâ (van Gelder and Port, 1995, p. 13).
Second language development (SLD)
The term SLD is often used in the study from the DST perspective rather than second language acquisition for two reasons: first, the language ability and performance of people change bi-directionally involving both growth and attrition, and the term âacquisitionâ is just associated with the unidirectional change. The use of SLD is also in alignment with Longâs (1993) much quoted definition as it includes the two directions of development:
The second reason is that from the DST perspective language is seen as an enabled process rather than a product or a thing. Larsen-Freeman (2010) prefers the term of language development to acquisition because open systems are never fully acquired. In the current study, the term SLD and SLA will be used interchangeably for, on the one hand, the dynamic process of language development is emphasized here; on the other hand, SLA has been extensively used in the previous research literature and it is not feasible to replace all the SLAs with SLDs.
Nestedness and ongoing interaction
A complex dynamic system (CDS) is composed of components or subsystems, and the components or subsystems are âoften interlinked on all possible levelsâ (van Geert, 2003, p. 658). These components or subsystems are not independent of each other and there are interactions within and between them. This quality is called nestedness. As for language, it is clear that it contains various structural linguistic components (and corresponding developmental processes). As Lowie et al. (2009) state,
They also indicate that âthe language system is nested within the cognitive system which is itself nested in the physical system of the bodyâ (Lowie et al., 2009, p. 140). In the present study, the L2 writing output is a complex dynamic system which is composed of the subsystems, such as vocabulary, syntax and discourse. Furthermore, these subsystems can be divided into smaller components. From the DST perspective, all these systems are inseparable, as pointed by Spivey (2007). But it is not possible to deal with all the nested systems at the same time and we have to focus on a certain number of aspects in our study.
Self-organization
Generally speaking, self-organization refers to the formation of the inner system structures. Organization can be divided into two types according to how they organize the inner structures: hetero-organization and self-organization. If a system organizes its inner structures according to external resources and instructions, then it is called âhetero-organizedâ; and if the increase of complexity is independent of the external source but arises from internal dynamics, it is called âself-organizedâ. From the DST perspective, self- organization refers to the developmental process of a system from simplicity to complexity driven by an inner mechanism. The phenomenon of self- organization is prevalent in human society, and self-organization makes systems maintain and generate new features.
Self-organization is a key feature in current cognitive theories (Smith & Thelen, 1993; Spivey, 2007; van Gelder, 1999) and can be applied in the study of language development. According to van Orden (2002) and van Geert (2003), language development is a process of self-organization. Larsen-Freeman and Cameron (2008) and de Bot et al. (2005) hold a similar view in their recent publications. Actually, this view is in line with emergentists and the usage-based view of language development, which puts the emergence in complexity due to its use. Since self-organization can explain the emergence of complexity without external influences, it has explanatory power to rival the supposition of an innate language acquisition device by Chomsky (1965). Self-organization plays an important role in building the complex structures of systems (van Geert, 2003).
Iterative growth
The growth1 of systems results from two factors: the preceding state of the system and the passing of time. As van Geert (2003) describes iterative growth:
Because of iteration, dynamic systems are sensitive to initial states. Subtle changes in initial conditions may have significant implications for future behavior of the system. This kind of sensitivity is often called the âbutterfly effect2â in weather systems (Lorenz, 1972). The change of dynamic systems may be sudden and unpredictable due to this effect.
Limited resources
Growth ârequires resources to keep the process goingâ (van Geert, 1995, p. 314). As for language learning, several kinds of resources are required: temporal resources, such as time spent on language learning; learner internal resources, such as motivation and capacity of working memory (van Geert, 1995). In DST, both external and internal resources enable the dynamic systems to develop. And in a particular study we can focus on a particular resource such as the influence of working memory on language learning.
According to van Geert (1995) âas far as the growth process is concerned, resources have two major properties. First, they are limited; second, they are interlinkedâ (p. 315). For example, in language learning the capacity of working memory is limited and the time allocated to a certain language item is also limited. In DST the limitations are called âcarrying capacityâ, which refers to the maximal growth potential of a system at some point of time given the available resources for its growth. Obviously, the carrying capacity is limited because resources are limited. From the DST perspective, the limited nature of resources is not necessarily a constraint for system development, but may be a key driving force. Resource limitations determine the interactions between the co-developing systemic components. Resource limitations may promote the interactions between components of systems and the components can increase or decrease simultaneously and support each other, forming a supportive relationship; they may also change inversely and compete for resources, forming a competitive relationship. These components are called âgrowersâ and the interactions between them are called âconnected growersâ.
Variability
Variability refers to the extent to which data points in a statistical distribution or data set diverge from the average or mean value. Variability is always viewed as ânoiseâ in traditional research and is often removed from data by averaging across samples. However, it may be precisely this variability that holds the key to how learning happens (Larsen-Freeman & Cameron, 2008). Variability is a key term in DST-oriented studies, which look on the variability patterns as self-organization arising from the interactions between components of systems.
Variability is the inherent property of system development, and the increasing variability within a system is a prerequisite for the qualitative change in the system. Variability can change t...