In the context of human development, identify a true statement about mechanistic researchers.

Abstract

Dynamic systems theory explains development as the probabilistic outcome of the interactions of processes at many levels and many systems. Its intellectual roots are traced to mathematics, astronomy, physics, meteorology, and biology. Contributions to the study of human development are introduced in the works of Esther Thelen who applied the theory to motor development, and Kurt W. Fischer and Thomas R. Bidell who applied it to cognitive development. Key concepts include systems, including open systems and the processes that preserve or undermine system stabilization; emergence; feedback; adaptive self-organization; nested timescales; disequilibrium; and the constructive web. The theory has informed analysis of dynamic skill development, parent-adolescent relationships, peer contagion, and antisocial development. The theory has guided multilevel interventions including effective support for school transitions. Approaches to measurement include case studies, mathematical simulation models, social network analysis, and state space grids. Strengths and limitations of dynamic systems theory are reviewed.

Dynamic Systems Theory

Dynamic systems theory conceptualizes smiles and other expressive configurations as constituents of infant emotional processes (Camras et al., 2018; Messinger et al., 1997; Thelen and Smith, 1994; Witherington et al., 2001). The process of smiling is part of the infant's experience of joy as well as an element in the infant's emotional communication with others. Dynamic systems theory focuses on the bottom-up interrelationship between smiles and other constituents of social interactions. This theoretical approach focuses on the temporal dynamics of smiles and positive emotional processes. The idea is that the formation of smiles during social interaction can provide insights into the emergence of smiling developmentally.

1.1 Foundational Concepts

DST has been applied to human cognition and development both as a conceptual framework and as a literal description of a dynamic system. We contend that both approaches are valuable and enrich our understanding. Our review of DST concepts is not an exhaustive list but instead focuses on those most foundational to the study of cognitive development. DST applications within psychological science have not been unitary. At the 2009 biennial meeting of the Society for Research in Child Development, a panel discussion of dynamic systems as a metatheory presented four “camps” of DST (see Witherington, 2007 for similar discussion). These camps all adopt the foundational concepts that we review here, but differ in the domains of application, the relative emphasis on different features of DST, and the philosophical perspective on what can (or cannot) be understood about the mental structures that underlie behavior (for further discussion see, e.g., Fogel, 2011; Hollenstein, 2011; Lewis, 2011; Spencer, Perone, & Buss, 2011; van Geert, 2011; van Geert & Steenbeek, 2005; Witherington & Margett, 2011). We come from the “Bloomington camp” associated with Thelen and Smith, and therefore primarily present examples from this “family” of researchers. Although we acknowledge the differences between camps as meaningful and consequential for research programs, we see great value in integrating conceptual and methodological variants across camps to achieve our ultimate goal: to understand how development happens. In the context of explaining cognition and development, we consider three concepts to be central: multicausality, self-organization, and the nesting of timescales.

The foundational DST concept of multicausality refers to the convergence of multiple forces to create behavior. The contributions to behavior in the moment include a person's body, age, mental state, emotional state, social context, personal history, and more. Furthermore, in dynamic systems no single factor is more important than any other—only through the combination of all factors together does causation occur, so it is illogical to consider any given factor in isolation. Proponents of DST emphasize an appreciation for mutual, bidirectional dependencies between brain and behavior, rather than considering behavior to be driven primarily by a single component (i.e., the brain). This aspect of DST has sometimes been criticized as making research intractable, as it is impossible to measure or control every potential contributing factor. As we illustrate in subsequent sections, however, we contend that multicausality can inform research design, implementation, and interpretation through the questions we ask with our studies, the way in which we gather information, and how we extrapolate from our results.

A second foundational concept is self-organization. The behavior of a system is an emergent product of multiple components interacting through time, interactions that are context dependent. Self-organization is related to a collection of additional DST concepts. Systems organize into what are called attractor states, which are ways in which the components of a system reliably interact (e.g., crawling, walking, and running are different attractor states for locomotion). Systems are historical, which means that their organization in an attractor state in the moment biases them to revisit those attractor states at a future point in time (Spencer & Perone, 2008). These states become increasingly stable through experience, which means that they are resistant to perturbations from internal and external forces. Systems are open to the environment, which means that external forces can shift the components of a system into a new way of interacting, which can often be nonlinear.

The last foundational concept is the nesting of timescales. The timescale of neural firing is nested within the timescale of cognition, which is nested within the timescale of behavior over learning and development. The strong claim of DST is that these timescales create each other. Consider a prevalent example from developmental science. Typically, we study children's behavior in the lab at one point in time and then at another point in time. This provides good insight into developmental differences. Developmental change, however, happens in between lab visits via massive quantities of real-time processes that occur across multiple levels. How do the neural processes, brain-wide dynamics, and movement that are involved in the behavioral decisions children make on a daily basis create developmental change? This is a central challenge for DST. This is illustrated in a case study described in a subsequent section that uses a computational model of infant looking behavior.

The three central concepts we described here—multicausality, self-organization, and nesting of timescales—are each interconnected in the empirical phenomena that illustrate them. Thelen's early application of DST concepts to development was in the motor domain, considering changes in infants’ stepping, reaching, and posture (see Spencer, Clearfield, et al., 2006 for review). But this subdomain of developmental psychology had become increasingly distant from the study of infant cognition, as researchers began to posit more complex and mature “concepts” that supported infant behavior. A critical challenge for DST was to move from the mechanics of motor development—where analogies to physical systems were easier to understand and appreciate—into the domain of human thought, which is often treated as qualitatively different from motor behavior. A first step in this direction was taken as Thelen, Smith, and colleagues applied DST concepts to Piaget's A-not-B task, purported to index the concept of object permanence in infants. This work illustrated the parallel between motor and cognitive development and, critically, their inseparability. Thus, we turn to a discussion of the Piagetian A-not-B error as an influential and historically important application of DST.

6 Dynamic Systems Theory

Dynamic systems theory has also influenced our thinking about the hierarchical organization of families and of time, as well as our conceptualizations of change. In particular, dynamic systems principles are well suited to examining complex questions about the interrelatedness of the whole and its parts (Bogartz, 1994; Smith, 2005), and thus, provide an ideal framework for research on family influence processes (Granic, 2000; O’Brien, 2005). Thus, we draw on dynamic systems principles in addressing the hierarchical organization of families, with multiple individuals and relationships nested within families, and the hierarchical organization of time, with multiple time scales nested within one another.

Dynamic systems theory addresses the process of change and development, rather than developmental outcomes; in dynamic systems terms, there is no end point of development (Thelen & Ulrich, 1991). Moreover, with its central focus on change and change in the rate of change, dynamic systems theory points to questions about both (a) change from one time point to the next; and (b) overall patterns of change. Chief among the contributions of dynamic systems theory is a set of concepts facilitating examination of overall patterns of change. Such patterns include stabilization, destabilization, and self-regulation.

In a ground-breaking application of dynamic systems theory to the field of developmental psychology, Thelen and Ulrich (1991) described motor development as the process of repeated cycles of stabilizing and destabilizing behavior patterns. In terms of social development, relationships may develop partly as a function of stabilizing and destabilizing behavior patterns of family members. For example, when parents repeatedly respond sensitively, their infants develop stable views of their parents as dependable. Moreover, family relationships may be self-regulating, with tendencies to return to baseline levels of functioning. As an illustration, a mother and her adolescent might have a fairly close relationship, but there may be periods of more or less closeness; that is, the system may oscillate back and forth past its baseline level of closeness. Thus, dynamic systems principles and methods afford opportunities to deepen conceptualization and empirically based knowledge of family influence processes. However, dynamic systems methods rely on mathematics-intensive procedures, and relatively little research has utilized this approach.

Dynamic systems theories

Dynamic systems theories consider development as a probabilistic outcome of the interaction of processes at many levels and many systems. The dynamic systems perspective can be applied to any system that changes overtime, from the cellular level to the solar system. However, its relevance to adolescent development has become increasingly useful as it suggests a way to coordinate moment-to-moment change with longer-term developmental transformations. Dynamic systems theory approaches this time of life as a phase transition that results from forces within and outside the person, merging and influencing each other to produce new capacities and behaviors. The chapter examines characteristics of open systems, adaptive self-regulation and adaptive self-organization, and the idea of the norm of reaction as these ideas apply to adolescent development. Three topics of particular relevance for understanding adolescent development have been examined from a dynamic systems lens: dynamic skill development; parent-adolescent relationships; and antisocial development.

1 General Considerations

Dynamic system theories share with neuroscience theories the adoption of models from outside of psychology itself. Although the neuroscience models are derived principally from biology, dynamic systems theories derive principally from physical theories, especially from principles of thermodynamics. The thermodynamics sources are not the traditional ones; rather they are modeled after recent chaos theories (Gleick, 1987). Related models have been applied in theories of biological development (Prigogine & Stengers, 1984), and earlier forms of these models have appeared in various disciplines (e.g., Thorn’s catastrophe theory). (See van der Maas & Molenaar, 1992, for an application of catastrophe theory to Piagetian stage development.)

I will cite three applications in developmental psychology (Thelen’s; van Geert’s; Garcia’s), A fourth (Ford’s) is from a social personality application of systems theory. The interest in them here is that they differ from one another in their assumptions about the structure–function relation, although they otherwise have much in common.

Dynamic systems theories, based on thermodynamic principles, deviate from the assumptions of strict causal explanation, in one sense at least. They deviate because, even when the initial conditions in a system and the rules of the mechanisms at play are known, the system always contains an element of uncertainty. Thus, totally accurate predictions based on that knowledge are not possible, although even in strictly causal systems there are limits to what is predictable.

Further, systems are defined as either integrated or composite and are said to be made up of elements that are organized into structures of one or another hypothesized type (e.g., fractals, trajectories, cycles), that are acted upon by hypothesized processes that move the systems from one state to the next. Nevertheless, it is not often the case that such processes are specified. For example, Kauffman (1991), developed a theory of biological evolution in which a model of weakly chaotic systems is applied to evolutionary data, but he gave details about only the logical relations among states and not the specific mechanism propelling the system on its trajectory. Thus, despite the language of dynamic “attractors,” and reference vaguely to the process that moves the system along, the process that impels development is not specified. This theory, as well as the physical dynamic systems theory of Bak and Chen (1991), and others, imply that the system is self-organizing and therefore “naturally evolves” (Bak & Chen, 1991, p. 46). Such a system is organized around the distribution of energy inherent in the system, as in a coiled spring, or around the energy inherent in downward flowing sand impelled by the force of gravity. The epistemic function of dynamic systems theory is to explain how such energy is organized within the system, how it acts upon the structures of such systems, and how the system functions in varying physical or biological conditions.

5.4 Dynamic systems models

Dynamic systems theories conceptualize development as change within a complex system that involves interactions of multiple factors at different levels and on different timescales (e.g., Smith & Thelen, 2003; Spencer, Austin, & Schutte, 2012). Thus, dynamic systems theories are well suited to conceptualize the interactions of multiple factors in processes of strategy change. Within dynamic systems theories, one key idea is self-organization, which is the idea that patterned behavior emerges out of the interactions of multiple elements of the system. Patterns of behavior are not specified in advance, but instead, they are “softly assembled” in the moment, depending on the specifics of the task, the context and setting, and the immediate and developmental history of the individual. Further, within any set of possible behavior patterns, some patterns are more likely to emerge than others. These common patterns are conceived as “attractor states,” to which the behavior of the system is drawn.

Empirical studies motivated by dynamic systems theories focus on how different factors interact to drive performance (Spencer, Perone, & Buss, 2011). Within dynamic systems theories, these factors are sometimes termed control parameters, because they “control” which behavior pattern emerges—that is, they control which of the possible behavioral forms the system displays. Control parameters may include factors at different levels and on different timescales. For example, in research on infants’ reaching, Clearfield, Dineva, Smith, Diedrich, and Thelen (2009) considered factors that operate on the timescale of the individual reach (e.g., the salience of a cue to reach to a particular location), as well as factors that operate over the set of reaching trials within a session (e.g., motor memory for previous reaches).

A similar approach could be applied to conceptualizing how different types of factors interact to drive strategy use and strategy change. Relevant factors operate on the timescale of the individual problem (e.g., Is there c ontextual support for encoding problem structure? Was feedback provided on the previous trial?) and factors that operate over longer timescales (e.g., Does the learner possess relevant knowledge for implementing a specific strategy? Is the learner highly confident that a particular strategy is correct?). Common strategies can be viewed as “attractor states”—highly probable behavioral states, to which the behavior of the system is drawn. Certain levels of specific factors may “push” the learner toward certain attractor states (i.e., toward using particular strategies) or “pull” the learner away from particular attractor states (i.e., away from using particular strategies).

As a representative example, consider mathematical equivalence problems with addends on both sides of the equal sign (e.g., 3 + 4 + 6 = 3 + __). The common incorrect and correct strategies that learners use can be conceptualized as attractor states; for example, the add-all strategy is one such attractor state, and the equalize (i.e., make both sides equal) strategy is another. Certain levels of specific control parameters may push learners toward the equalize attractor state; for example, contextual support for encoding the position of the equal sign encourages learners to generate the equalize strategy (Alibali et al., 2018). When solving a problem, if a learner lacks confidence in their current strategy—a metacognitive judgment that might reflect that the attractor state that gave rise to the strategy was relatively weak—this may make generation of a novel strategy in the context of perceptual support even more (or less) likely. Likewise, if a learner does not have the requisite mathematical skills to implement a particular strategy (an individual difference factor), this may prevent that behavioral form (i.e., use of that strategy) from emerging.

From a dynamic systems perspective, individual difference factors, contextual factors, and metacognitive factors are all control parameters that may push the system toward or away from particular attractor states. These factors converge for any given individual at any particular moment—sometimes in nonadditive, nonlinear ways—to yield behavior that (usually) aligns with a patterned form of behavior that is recognizable as use of a particular strategy. Thus, changes in the levels of different control parameters may—or may not—yield changes in the behavior that emerges. Factors of different types and at different timescales interact to give rise to behavioral forms that reflect particular strategies, which may represent consistent strategy use or strategy generation for a given individual at a given point in time.

Some scholars have sought to formalize dynamic systems accounts in computational models (e.g., Samuelson, Spencer, & Jenkins, 2013; Simmering, 2016). Importantly, such models can be used to make predictions about performance and change that can then be put to empirical test. If applied to research questions about strategy change, such an approach holds promise for shedding light on how multiple factors interact to explain processes of strategy use and strategy change.

Dynamic systems theory

DST asserts that human development must be conceptualized as the “multiple, mutual, and continuous interaction of all the levels of the developing system, from the molecular to the cultural” (Thelen & Smith, 2006, p. 258). Furthermore, the DST perspective holds that the process of human development is a continually self-organized one and the dynamic nuanced product of patterned interactions between multiple parts of an interconnected micro- and macrolevel system (Thelen & Smith, 2006). Thelen and Smith employ the use of the mountain stream as a metaphor to illustrate the variety of proximal and distal variables that synergistically interact to determine human development. This metaphor is useful in understanding the “dynamic cascade” of development (Thelen & Smith, 2006, p. 263). Rather than following a linear approach that identifies isolated, seemingly static, developmental ingredients, this model highlights the continuously evolving and interdependent nature of contributing developmental processes. Furthermore, dynamic system theorists recognize that the developmental outcomes being seen in the here-and-now are the product of pervasive current and historical patterns which continuously influence and co-construct the present. The mountain stream metaphor is useful in conceptualizing these ideas: current weather patterns that influence how quickly (or slowly) the mountain snow melts to create the stream, the molecular composition of the water and how this impacts the pace and flow of the current, and the mountain’s vegetation and its impact on evaporative processes. Historical geological factors that act over periods of time also help to shape present-day patterns. Thelen and Smith (2006) provide but one illustration of this interdependent process: “the long-range climate of the region led to particular vegetation on the mountain and the consequent patterns of water absorption and runoff” (p. 263).

Applying this metaphor to developmental psychopathology research, a more simplistic linear causality approach to disruptive behavior problems is insufficient to capture the complexity and dynamism of the human developmental process. As illustrated in previous chapters, it is evident that no one factor or process is necessary and sufficient for the development of disruptive behavior problems in youth nor does any particular model account for the entire proportion of the variance in the manifestation of disruptive behavior problems. The complexity inherent to these problems calls for a lens of examination that considers inextricable, active components. DST provides a framework through which to consider the multiple pathways of effective intervention at both macro- and microlevels.

With this theoretical perspective in mind, the purpose of this chapter is to present the macro (often referred to as social determinants) that have been examined as potential attractors that either push children towards or pull them away from developmental trajectories that perpetuate problematic and disruptive behaviors. A number of microlevel factors/mediating mechanisms such as temperament, callous/unemotional traits, and attributional bias have been identified as factors that potentially impact the development and maintenance of disruptive behavior problems; we refer readers to chapters in this book for a comprehensive review of these microlevel factors (see Chapters 5–8Chapter 5Chapter 6Chapter 7Chapter 8: Negative affect, Callous–unemotional traits, Cognitive attribution bias, and Sensation seeking and risk-taking, respectively). Relatedly, broad-based contextual and systematic considerations such as social determinants of health have also been studied to inform how elements of broad factors (e.g., housing) impact and how disruptive behavior problems develop, and these macro factors/social determinants are the focus of the remainder of the chapter. The authors aim to present the various leverage points in the complex developmental system from which researchers have approached intervention work. Thus, we encourage the reader to digest the following research with the preface that each intervention is but one way of approaching a complex problem

Dynamic Systems Theories

Dynamic systems theories are complex and sophisticated, but we can present the essential ideas. Technically, a dynamic system is a formal system the state of which depends on its state at a previous point in time. Dynamic systems are self-regulating, meaning that they are the result of the interaction of variables, and processes, which combine spontaneously to achieve a stable state or equilibrium. One reason why dynamic systems are important to cognitive development is that they can account for different types of cognitive growth that have been observed. That is, development is sometimes slow and steady, while at other times sudden jumps occur, resulting in new levels of functioning that appear quite different from anything that was there before. This is what led theorists like Piaget to propose that cognitive development occurs in stages, such that entirely new cognitive processes emerge when the transition is made to a new stage. Dynamic systems can show how a complex, self-regulating system can emerge from the interaction of a few variables, and offer natural interpretations of concepts such as equilibration and self-regulation which are at the core of the theories of both Piaget and Vygotsky. Links have also been made between dynamic systems models and neural net models, to be considered below.

An example of a dynamic system would be children's acquisition of the concept of conservation, considered earlier. Children of 3–4 years of age typically think that, when liquid is poured from a short and wide to a tall and narrow vessel the quantity increases, because they see the large increase in height. Understanding that the quantity remains constant typically develops spontaneously, and often appears quite suddenly, so that in a short time the child might switch from being sure that the quantity increases to being sure that it is constant. What appears to happen is that the children start to relate the three variables of height, width, and quantity, as mentioned before. That is, they realize that when you take both height and width into account, quantity remains constant, or is “conserved.” Here the three variables are brought into a new integration, which creates a new form of stability. These variables are also related to observations that nothing was added when the liquid was poured, and that it would be same again if poured back. Quantities that formerly seemed to increase or decrease as liquids were poured from vessel to vessel are now seen as invariant over those transformations, and a lot of additional information is integrated with this conception. This development is spontaneous and is not usually taught. Indeed, attempts to teach it might be ineffective until the child is ready to make the new integration. This illustrates the self-regulating nature of cognitive development.

2 Dynamic Systems Theory: periodic Forcing of Oscillators

Dynamic systems theory studies the behavior of systems that exhibit internal states that evolve over time (i.e., internal dynamics) and how these systems interact with exogenously applied input (often referred to as perturbations). The main language used is differential equations that describe the evolution of a system by formalizing how the state variables that describe the system change over time as a function of the internal state and external input. Here, we limit ourselves to a qualitative introduction and closely follow the excellent approach by Pikovsky et al. (2001) to provide the fundamental vocabulary and concepts needed to then discuss the behavior of brains in both experiments and computational simulation.

An oscillator is a system that generates a rhythmic activity pattern fueled by an internal energy source. Importantly, the periodic motion of the oscillator is not simply the reflection of a periodic input since an oscillator is self-sustained. Oscillators have an oscillation period T and the associated frequency f = 1/T. The natural frequency denotes the oscillation frequency of an oscillator in the absence of external input or perturbations. Synchronization can be defined as the change in rhythmic activity induced by interaction of an oscillator with another oscillating system (e.g., two oscillators, or an oscillator and external periodic stimulation). Phase locking or entrainment denotes the behavior of two interacting oscillators that exhibit a (near) constant phase offset (technically, 1:1 locking). In the context of this review, synchronization of an oscillator by an external force is the key concept for which dynamic systems theory provides important guidance for the mechanistic study of brain stimulation for the perturbation of rhythms. In its most simple form, both the oscillator and the periodic force can be described by a sinusoidal oscillation. The frequency of the oscillator and the periodic force do not always match, and the difference between the frequency of the oscillator (f0, natural frequency) and the frequency of the periodic input f is called detuning, f–f0. The response of an oscillator to a periodic force then is typically described as a function of the detuning and the strength of the perturbation, often denoted as an amplitude ɛ.

For a given (weak) strength of the periodic perturbation, two distinct behaviors can emerge as a function of the amount of detuning (Fig. 1). The force by the external perturbation tries to get the system to synchronize to the driving oscillator such that the difference in the phase between the oscillator and the perturbation is stable and the phase of the oscillator locked. In contrast, the mismatch in frequency between the oscillator and the periodic perturbation (i.e., the detuning) pushes the phase of the two oscillators apart. At some point during an oscillation cycle, the perturbation force acts in the opposite direction of the push by the detuning and—when in balance—synchronization (entrainment) occurs such that the oscillation frequency of the driven oscillator matches the stimulation frequency (synchronization). In case of large detuning, the periodic force is not strong enough to counteract the divergence of phase caused by detuning. Thus, the force is not strong enough to enable synchronization and the resulting frequency of the system will be somewhere between the natural and stimulation frequencies. However, the resulting dynamics are more complicated since there is acceleration and deceleration; the oscillator slows down in the region where the perturbation force and the detuning are closest to canceling each other out and accelerates when in the region where the force and the detuning are additive.

Of importance, this model assumes that perturbations only alter phase and do not significantly alter the amplitude of the oscillator. In other words, the amplitude is fixed (stable) and phase is (in the absence of an external perturbation) a free parameter. Also, the above reasoning applies to linear or “quasilinear” oscillators. Strongly nonlinear oscillators exhibit no circular limit cycles, and the phase progresses at a nonuniform rate.

Periodic external perturbation can often be conceptualized as a series of pulses. Importantly, the same pulse can cause either a phase advance or a phase delay depending on when it is applied. The larger the perturbation amplitude, the larger the resulting phase change. Therefore, if pulses are applied such that they counteract the phase difference that results from the detuning, the two systems can synchronize at the frequency of the stimulation. The above introduced effects of stimulation amplitude and frequency lead to so-called Arnold tongues that describe the set of parameters that lead to synchronization (Fig. 1C). This parameter set can be visualized as an area in a plot which exhibits stimulation frequency on the abscissa and stimulation amplitude on the ordinate. The larger the stimulation amplitude, the broader the range of stimulation frequencies at which the oscillator entrains to the stimulation; thus, the area takes the shape of an inverted triangle (hence the name “tongue”).

In the following sections, I will review human, animal model, and computer simulation studies and discuss the findings in the context of the synchronization mechanism described here. Schematic representations for the in-depth discussed studies are presented in Figs. 2–4. Most findings fit the Arnold's tongue conceptualization. However, as we will see, (1) most experimental studies (for practical reasons) do not provide sufficient parameterization and (2) several findings likely require more sophisticated and less intuitive models (denoted as thought-provoking ink blots in Figs. 2–4).