## Dynamical Systems Theory Definition

Emotions go up and down over the course of days. But sometimes emotions are more constant. For instance, depression could be characterized with fairly constant negative emotions across days. When will hearing some negative information lead a person into a depressed pattern? When will the same negative information just lead to a bad day among the good days? Dynamical systems theory (also known as dynamic systems theory or just systems theory) is a series of principles and tools for studying change. It is based on concepts from mathematics and is a general approach applicable to almost any phenomenon.

There are two types of change that are central to this method. First, a systems approach focuses on how a phenomenon changes over time. For example, a systems approach to emotions concentrates on how emotions evolve in time rather than whether a person is happy or sad on a given day. It seeks to identify patterns of change that can be reoccurring, constant, or even ever-changing. For example, emotions might go back and forth between good and bad days (reoccur-ring), remain negative (constant, not unlike depression), or constantly change in complex ways. A systems approach often assesses the stability of those patterns. For example, will receiving some negative information knock a person out of a pattern of ups and downs? Will the same negative information disrupt a constant negative pattern such as depression? Dynamical systems theory can also identify when the pattern of emotional change will evolve into another pattern on its own or in relation to other parts of the system. For example, under what circumstances can only a constant negative pattern of emotions exist? In summary, dynamic systems can be used to identify what might alter the entire long-term pattern of emotions that follow.

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The second type of change examined by systems theory is that which occurs from the many interactions among units (i.e., individuals, groups, aspects within the individual). For example, a systems perspective of emotions might simultaneously consider the interaction of the differing emotions between a husband and wife. These interactions are assumed to be multidirectional. That is, the husband and wife mutually influence one another so that each changes and limits the emotions of the other. Because of these mutual influences on emotions with other people, there is the potential for each person to generate a very complicated pattern of emotions in time. Surprisingly, these multicomponent systems tend to generate relatively simple patterns. For example, a pair of individuals who begin with different emotions might converge on the same emotional pattern and might even help each other maintain that pattern (stability). That is, a couple both in the same ups and downs of emotions might make each person in the pair more resistant to negative information. This order emerges because of the multidirectional and reciprocal influences and tends to promote a great deal of predictive power. For example, you might need to know only the emotional pattern of a single individual in a group to know automatically the emotional changes of every other individual in the group. Thus, part of a systems perspective is identifying the qualities that depict the entire multicomponent system.

## Context and Importance of Dynamical Systems Theory

Within social psychology, systems theory has been applied to a wide variety of topics. It is often called a meta-theoretical perspective because its principles can be applied to virtually any phenomenon. For this reason, systems theory is often thought not to be theory at all but instead a descriptive tool. Regardless, systems theory is inherently an interdisciplinary approach found in fields as diverse as mathematics, physics, architecture, biology, chemistry, and psychology, sharing the same language, tools, and concepts.

## Dynamical Systems Theory Applications

Systems theory tends to be applied in three main ways. The first, dynamical systems modeling, consists of generating simulations of the many interactions functioning over time. The simulations describe the phenomenon mathematically, testing out situations that parallel the real world but that would be difficult to study in the real world. For example, it is possible to study the emotions of couples across days, but modeling could be used to examine emotions at a community level identifying the circumstances that discriminate when depression is commonplace in a community from when it is rare. Dynamical systems models have revealed that very simple mathematical equations of change are capable of producing a great deal of complexity. The simulations need not be very complicated to move beyond predicting patterns in real life. However, both relatively simple equations and very complex ones can also generate order.

The second way dynamic systems theory is used is empirically. In empirical methods, mathematical concepts are applied through longitudinal methods and designs that measure changes over time. These studies tend to be very data demanding, often collecting information in real time over long periods of time. Mathematical equations and systems concepts are then used to describe the outcomes, often generating new predictions for further empirical studies.

Lastly, systems theory is used as a metaphor whereby the concepts are applied qualitatively without use of mathematical relationships. Many phenomena in psychology cannot easily be measured at the quantitative level that is demanded by empirical systems techniques. Nor can they be easily quantifiable by a set of equations. Thus, the concepts are used as heuristic examples of the phenomenon. Since a systems approach focuses on change and complex interactions, the concepts are still metaphorically informative to the psychological sciences.

### References:

- Gottman, J., Murray, J., Swanson, C., Tyson, R., & Swanson, K. (2002). The mathematics of marriage: Dynamic nonlinear models. Cambridge: MIT Press.
- Kauffman, S. (1995). At home in the universe: The search for laws of self-organization and complexity. New York: Oxford University Press.
- Kelso, S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge: MIT Press.
- Nowak, A., & Vallacher, R. (1998). Dynamical social psychology. New York: Guilford Press.
- Stewart, I. (2002). Does God play dice? The new mathematics of chaos. Malden, MA: Blackwell.