Introduction to the Section: Nonlinear Dynamic Systems Theory

ABSTRACT

Nonlinear Dynamic Systems Theory is discussed by three child, adolescent, and adult analysts who use this theory in their thinking about development from infancy through old age and as a way of understanding the process of change in psychoanalysis. This theory explains how the systems of the brain, the body, the environment, and the culture interact and help determine character formation throughout the life cycle. Examples of development and psychoanalytic treatment are used to demonstrate the application of nonlinear dynamic systems.

KEYWORDS:

• Nonlinear dynamic systems theory
• development
• chaos
• psychoanalysis

This section started out as a panel presented at the 2022 Boston meeting of the American Psychoanalytic Association. Erik Gann, on behalf of the Committee on Psychoanalytic Education, invited Robert Galatzer-Levy, Stephen Seligman, and myself to present nonlinear dynamic systems theory (NLDS) as a means of informing analysts about this theory and broadening their theoretical understanding of development and this theory’s application to their clinical thinking and work. We were asked to discuss how we became interested in NLDS, give an example of how it informs our clinical work, and propose how it changes and/or adds to the body of psychoanalytic scholarship and clinical practice.

Nonlinear dynamic systems theory comes from the mathematical study and understanding of complexity and chaos. It is the study of how a system changes over time and the complex interaction of systems over time. Bertalanffy (1968) was amongst the first to apply dynamic systems to understand human development. Edelman (1987), working in the area of genetics and memory, proposed that there are genetically defined regulatory systems in human development that make order out of the chaos of incoming stimuli. A very complex interaction between these internal processing and regulating systems already exists at birth. Meltzoff and Borton (1979) demonstrated that babies who explored objects by touch alone could then recognize those objects visually, suggesting that there is reciprocal assimilation and accommodation of information in the visual and motor systems. Thus, change in one organizational system can also modify other organizational systems, indicating that the infant is already biologically wired to organize and abstract the chaos of incoming stimuli.

This complex interaction between biological systems also exists between biological, environmental, and psychological systems. An extensive literature in psychosomatic research delineates the interrelated effects of environmental changes, behavior, and the body’s biochemistry (Hofer 1981). Advances in nonlinear statistical models (Lewis, Lamey, and Douglas 1999; Sharfstein 1996) have given us the statistical tools to study the multiple forces influencing the changing patterns in these structures, as well as their coordination, greatly enhancing our ability to understand the development of organizational and regulatory systems, both individual and interactional. By the 1990s Thelen and Smith (1994) were conducting cognitive and behavioral development research on infants and toddlers that demonstrated the relevance and utility of a nonlinear dynamic systems theory adapted from mathematical chaos theory.

Nonlinear dynamic systems theory proposes that the continuous interaction of biology and environment produces a complex interplay of systems that are fluid, variable, function-driven, flexible, and nonlinear. This interplay of systems leads to emergent development. In development there are periods of significant disorganization in which structural systems break down and reorganize in transformational ways. New information from the body and the environment is assimilated and accommodated by increasingly complex systems in the mind and body. Stable configurations of cognitive, biological, and emotional systems suddenly become destabilized for no outwardly apparent reason and shift into periods of fragmentation before a new equilibration of the system or systems is achieved. Galatzer-Levy (2004) describes it as a system constantly on the edge of chaos. Essentially growth is observed by the complexity and coherence of the developing systems over time. In terms of psychological growth, each novel state is progressive, discrete, idiosyncratic, nonlinear, and unpredictable.

In a dynamic system of development, stabilization points must be reached to manage the continuous onslaught of new information and the disturbance and reorganization of internal structures caused by incoming information. In Piagetian terms (Piaget 1967), equilibration must take place before new information can be assimilated and accommodated in ongoing dynamic structures. Thus, a certain degree of stability is necessary for optimal learning and development. However, a person who is too consistently stable, or rigid, would not allow new stimuli to disturb his or her equilibrium so that change can occur. A person whose internal organization shifts with every new stimulus would not allow for the time necessary to take in new information and alter systems to accommodate the incoming stimulus necessary for lasting change.

An optimal degree of flexibility, regulatory functioning, and equilibrium allows memories and behavior to become established and then allows new stimuli to be absorbed so that change can occur. The degree to which development is able to move forward depends on the degree to which a dynamic system can stably engage and flexibly switch over a certain period of time.

A nonlinear dynamic systems theory of development proposes that we are born with a genetic blueprint for development. However, this blueprint is a rough draft, an initial plan, from which more defined, individual systems will evolve as genes regulating development turn on or off based on environmental factors. These individual systems – cognition, actions, self-states, to name just a few – are influenced by the interaction of biology, psychic structures, and environment. As new stimuli from either biology or the environment are encountered these internal stable systems break down and a novel, functional alternative change in the systems develops to respond to the incoming stimuli. Changes in one system – let’s say cognition – can affect changes in other systems, such as self states, causing a cascade of changes within and between systems. In this manner a highly complex pattern of development emerges that produces an individualized response that is able to flexibly react to unusual circumstances in biology or the environment.

Time is also an important factor in system development, and researchers studying dynamic systems distinguish between real time (the immediate experiences an individual encounters in the physical, biological, and social environment that promote change), developmental time (the continuing prior and present experiences an individual encounters), and evolutionary time (the transgenerational effects of the individual’s experience). Behavioral change occurs at all three levels of time. Accounting for the dynamics of development at the real and developmental time level allows us to think about developmental change that happens over weeks, months, and years, and evolutionary time follows change that happens over generations and centuries. Development occurs over time in nested timescales, in which there is an immediate small response followed by larger and larger responses until a behavior is learned. For instance, in learning to read children first learn letters, then syllables, then words, then sentences. Each increasing development in reading is nested inside previous systems being formed. The same can be seen in psychoanalysis when people first hear an interpretation to when, over time, they can make use of the interpretation and eventually make the observation for themselves.

Complex systems can be linear, producing recognizable patterns of behavior, or they can be nonlinear (Emde and Harmon 1984), when small changes in a system can lead to large changes in behavior down the road – sometimes called “sensitivity to initial conditions” or the butterfly effect. It is often nonlinear changes in individual or interacting systems that lead to individual differences and make understanding individual development a messy undertaking. This is in keeping with Galatzer-Levy’s (2023) idea about treatment: that complex systems arise from a dyadic exchange that is often filled with periods of disorganized, messy, not knowing chaos that both participants have to tolerate. Smith and Thelen (2003) have a similar view of development: “In human development, every neural event, every reach, every smile, and every social encounter sets the stage for the next and the real-time causal force behind change. If this is so, then we will gain a deeper understanding of development by studying multicausality, nested timescales, and self-organization” (p. 347).

All three authors, in discussing how they became interested in NLDS, give examples of aspects of dynamic systems in development. Galatzer-Levy takes the reader on his developmental journey from his late adolescence to emerging adulthood. As he notes, he had gone through high school and his first year of college with a certain stability in his interests and character, a very stable attractor that doesn’t allow for much change during his freshman year. His roommate and his dreary courses don’t provide enough spark to change any aspect of his cognitive or social systems. Unpredictably, his sophomore roommate arrives on the scene. Their interests are compatible and they become fast friends. Added to this are two courses, one in higher mathematics and one in introductory psychology. Between the evolving love for a friend, the excitement and love for mathematics, and the fascination with psychology Galatzer-Levy’s cognitive, psychological, and social systems assimilate the new information both individually and interactionally. The changes are so great that the systems need time to accommodate the changes and, as he says, they then become attractor states. Without giving the plot away (though we all know how the story eventually ends), having to choose a life course, and his experiences of going to school in NYC’s Village in the 1960s, brought him to the edge of chaos “where the breakdown of preexisting order results in the emergence of more complex, often nonlinear, processes” (this volume, p. 7). It is a complex (and amusing) story that explains the basic concepts of NLDS and gives the reader an experience-near description of a period in development understood through NLDS that is unique in its presentation, educational in its content, and takes you inside the mind of Galatzer-Levy, demonstrating the complexity of nonlinear dynamic systems and its formation from higher mathematics.

Stephen Seligman focuses on his personal experiences as a child and adult analyst, showing how he uses NLDS to think about his patients and the way he thinks about and practices psychoanalysis. He points to the time spent in not knowing when doing analysis, when listening often involves messy, peculiar, and chaotic thinking before an idea or change in the patient will take shape, often with no understanding of how that change occurred from the analytic process, change that is “unpredictable, emerges in fits and starts, often along with surprise and disorientation in both (or either) patient and therapist” (this volume, p. 3). He notes that NLDS helps explain how that change occurs.

His professional experiences and his also growing up in the 1960s influenced his choice to work with infants and parents and to work with underserved communities. His abiding curiosity about how the social and political aspects of our environment influence our life’s course led to his interest in the interrelation of the intrapsychic, the social, and the biological. Seligman finds that NLDS is particularly good at focusing in on the interaction of all three in understanding both development and our patients.

He sees NLDS as a metatheory that incorporates many useful ideas and techniques in psychoanalysis while offering “a rigorous, elastic and spacious meta-framework for both psychoanalytic theory and practice … . and places shifts and uncertainty at its center in a framework that is also pragmatic, scientifically rigorous and experience-near” (this volume, p. 5). He stresses the need to focus on all aspects of a patient’s life – the biological, psychological, social, environmental, cultural – in order to comprehend how all of those systems have interacted and influenced the strengths and weaknesses of the people we treat. He uses case material from an eight-year-old boy where little progress in treatment could happen until his learning disability was remediated as an example of the interrelatedness of the neurobiological and intrapsychic systems, something many child analysts experience in their treatment of children with learning disabilities.

For Seligman, the beauty of NLDS is its ability to incorporate and analyze every aspect of a person’s life. An activist also interested in psychology and human relations, he is particularly interested in integrating analysis with the social and political aspects of the people he treats and sees understanding the interrelatedness of those two systems as “an essential, if neglected potential for our field” (2023, p. 4). To that effect, he describes a case in which race, socioeconomic class, and the bureaucracy in the social systems in our country interweave, causing pain and anger that is both chronic, immediate, and complex to treat. He notes that sometimes giving some educational help can be the tipping point for change.

My paper starts by describing the unexpected influences that led me into research and then to NLDS. Most notable was my psychology 101 class in college. I had planned my whole life intending to become a writer, had completed my college major in that field, and had begun publishing my work. Talk about a strong attractor! I left all my required courses for the end of my college career. Psych 101 was required and took place in a huge lecture hall with 350 students. I found it fascinating, even learning about perception was fascinating. I developed the first major conflict of my life (writing vs. psychology) and went into therapy, which proved to be even more fascinating. We all know how this story ends as well. Along the way my life required a flexibility so that I could avoid the pitfalls while taking advantage of the immediate experiences I encountered along my developmental route.

Spending so many years doing a longitudinal research project while in analytic training and not having any idea of what to make of the data was challenging. Learning about NLDS opened up a way to look at my data that was both exciting and thought provoking. Complexity theory requires looking at many different systems on many different levels across different times. I had collected the data to be able to do that, and when I finally got the hang of it, it felt like I had discovered a treasure. Not only was this theory a solution to understanding my data in depth, it was a way to understand development, my patients, and how the world works.

All three authors had unpredictable experiences that influenced our lives and our careers and led us to a theory that explained nonlinear development and the overarching complexity of psychoanalysis. It is no surprise that the contributors to this section are all child analysts. We engage with changes and interactions with the biological/psychological/environmental/cultural systems all the time in our work. We have to get involved in the real lives of our patients: parents, siblings, peers, school, doctors, learning specialists, etc. all the time. We literally watch, engage with, and help promote development in our work with our patients. It is easier for us to grasp the idea of interacting systems over time.

It is my hope that this section makes its way out of the hands of child analysts and is read by analysts of adults who get as excited by this theory as we are. Development and psychoanalysis are both complex, overarching processes and nonlinear dynamic systems theory helps guide our understanding of them both.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Rona Knight

Rona Knight, PhD, is a child, adolescent, and adult psychoanalyst. She is an assistant professor of pediatrics and psychiatry at the Boston University School of Medicine, a faculty member and child supervisor at the Boston Psychoanalytic Society and Institute, and a senior editor of The Psychoanalytic Study of the Child.