Applying dynamic systems theory and complexity theory methods in psychotherapy research: A systematic literature review

Figures & data

Table I. Descriptive information about all studies included in the review.

ID /#	Reference	Country codes (1b)	Mathematical methods and models (2a); (2b) [(2c)]; (2d), (2e); (2i)	Psychotherapeutic phenomena (3a); (3b) [(3d)]	Software (4b)	Data (5b); (5a); (5c) [(5d)]
1	Baker (2018)	United States of America	1; stable attractors, emotion inertia, critical points, interpersonal influence based on emotional valence [Gottman’s differential equations model]; ODE, first-order; Ch = 0	2; therapeutic relationship as client-therapist affects interaction [cognitive, psychodynamic, emotion-focused therapy—0]	MATLAB, SPSS	1; video-transcripts; 1 [n = 2]
2	Bob (2007)	Czech Republic	3; self-organization of behavior during critical periods, chaotic patterns and state transitions [Lyapunov exponents, false nearest neighbors and embedding dimension]; NA; Ch = 1	1; physiological emotion-related sympathetic activity [hypnosis—0]	Dataplore	1; audio-/video-transcripts, electrodermal aktivity; 0 [n = 2]
3	Brice (2019)	United Kingdom	1; dynamics of treatment pathways [agent-based model, system dynamic model]; ODE, first-order; Ch = 0	1; depression [CBT—1]	R	Only simulated data
4	Buckman et al. (2018)	United States of America	NA; NA [computational physiology model of baroreflex on cardiovascular system]; NA; Ch = 0	1; physiological arousal, baroreflex, heart rate [behavioral biofeedback—0]	NA	1; baroreflex physiological states; NA [n = NA]
5	Burger et al. (2020)	Netherlands	1; rate of change, decay, inertia and influence of other variables [differential equations model, computation model of functional analysis to create a formal theory]; ODE, first-order; Ch = 0	1; anxiety, avoidant behavior, perceived benefits or costs of coping, credibility of catastrophic interpretation [CBT exposure and cognitive reappraisal—0]	R	Only simulated data
6	Fisher et al. (2011)	United States of America	1; degree of order, patterns in dynamic system, rank-order differences, intraindividual variations [spectral analysis]; NA; Ch = 0	1; anxiety [CBT, applied relaxation behavioral therapy—0]	LISREL	2; diary; 0 [n = 33]
7	Fuhriman and Burlingame (1994)	United States of America	NA; embedded patterns of order within and across sessions [sequential analysis of local patterns, correlation integral of global patterns—fractal estimates]; NA; Ch = 1	2; group verbal interactions [general therapy—1]	NA	1; audio-transcripts; 0 [n = NA]
8	Gumz et al. (2014)	Germany	1; topological complexity, degree of synchrony, discontinuous changes [dynamic complexity algorithm—fluctuation + distribution]; NA; Ch = 0.5	3; therapeutic relationship as client-therapist transference-countertransference interactions [psychoanalytic therapy—0]	NA	3; self-report questionnaire; 1 [n = 1]
9	Gumz et al. (2010)	Germany	1; topological complexity, discontinuous changes—abrupt vs. V-shaped changes [dynamic complexity algorithm—fluctuation + distribution]; NA; Ch = 0.5	3; therapeutic relationship as client-therapist transference-countertransference interactions [psychodynamic therapy—0]	NA	3; self-report questionnaire, video-transcripts; 0 [n = 6]
10	Haken and Tschacher (2017)	Germany	1; attractor dynamics, self-organization, agent responses, temporal evolution [synergetic computer algorithm based on differential equations]; ODE, second-order; Ch = 0	1; borderline personality disorder, cognitive-behavioral-experience psychological patterns [general thrapy—0]	NA	Only model for simulation
11	Helmich et al. (2020)	Netherlands	1; sudden changes, relative frequency of other types of therapeutic development change trajectories—null, linear, log-linear, stepped [linear regression on trend]; NA; Ch = 0	1; depression [integrative treatment mostly CBT, psychoeducation, physiotherapy, creative and psychomotor therapy—1]	R	2; self-report questionnaire; 0 [n = 329]
12	Jason et al. (2020)	United States of America	1; temporal evolution, change trajectories [differential equation model—conceptual dynamic influence model]; ODE, first-order; Ch = 0.5	1; alcohol/drug dependence, social support, abstinence self-efficacy, stress [community-based posttreatment support—1]	NA	Only simulated data
13	Kowalik et al. (1997)	Germany	3; critical state transitions, topological complexity, entropy variations in signal, chaoticity, sudden changes, chaos-to-chaos transitions, degree of synchrony [pointwise PD2 algorithm or correlation dimension, entropy rates, Shannon entropy, local Lyapunov exponents, plasticity of chaotic measures—relative-within-session and short-term]; ODE, first-order; Ch = 1	2; therapeutic relationship as client-therapist verbal and nonverbal interactions [solution-oriented therapy—0]	NA	1; video-transcripts; 1 [n = 1]
14	Laramée et al. (2016)	Canada	3; state transitions, fixed cycles, treatment discontinuations [Markov model, microsimulation model]; NA; Ch = 0	1; alcohol consumption, drinking patterns [alcohol dependence pharmacotherapy with psychosocial support—0]	NA	2, 3; daily alcohol consumption; 0 [n = NA]
15	Lauro Grotto et al. (2014)	Italy	3; second-order phase transitions in collective dynamics, degree of social mixing, evolution of the psychological state coupled with the evolution of the group-subjects affinity [agent-based model]; NA; Ch = 1	2; group behavior’s structured patterns based on cognitive-affective evolution [psychoanalytical Bion’s group therapy—1]	NA	Only simulated data
16	Li and Kivlighan (2019)	United States of America	1; mutual influence patterns, multilevel data disaggregation [Gottman’s differential equations model]; ODE, first-order; Ch = 0	2; therapeutic relationship as alliance—client’s perception of session quality [general therapy—0]	Hierarchical Linear Modeling software	3; self-report questionnaire; 1 [n = 180]
17	Liebovitch et al. (2011)	United States of America	1; stable attractors, emotion inertia, critical points, interpersonal influence based on emotional valence [Gottman’s differential equations model]; ODE, first-order; Ch = 0	2; therapeutic relationship as client-therapist affectivity interaction [integrated therapy—0]	MATLAB	Only simulated data
18	Lichtenberg and Knox (1991)	United States of America	2; randomness and disorganization of the group’s interaction [Shannon entropy]; NA; Ch = 0	2; group’s social interaction [Yalom’s group therapy—1]	NA	1; audio-/video-transcripts; 0 [n = 32]
19	Olthof et al. (2020a)	Netherlands	1; phase transitions, system reorganization, degree of destabilization and instability [dynamic complexity algorithm—fluctuation + distribution, peak complexity—relative strength of the highest peak in dynamic complexity profile]; NA; Ch = 0.5	3; depression, client’s cognitive-emotional dynamics [integrative therapy—0]	R	2; self-report questionnaire; 0 [n = 328]
20	Olthof et al. (2020b)	Netherlands	1; sudden changes, critical instability, early warning signals, local highest topological complexity, cumulative complexity peak [dynamic complexity algorithm—fluctuation + distribution, peak complexity—relative strength of the highest peak in dynamic complexity profile]; NA; Ch = 0.5	3; depression, client’s cognitive-emotional dynamics [integrative therapy—0]	R	2; self-report questionnaire; 0 [n = 328]
21	Orsucci et al. (2016)	United Kingdom	3; recurrence patterns, power law, autocorrelation decay [recurrence quantification analysis, autocorrelation analysis, Lempel-Ziv entropy, Shannon entropy, autoregressive models—ARMA, GARCH]; NA; Ch = 0.5	2; physiological client-therapist galvanic/linguistic skin response synchronization [short-term CBT—0]	MATLAB	1; audio-transcripts, galvanic skin response; 1 [n = 1]
22	Paz et al. (2021)	Israel	1; intra- and interpersonal damping—average and change in damping, relation to outcomes [dynamic systems model]; ODE, first-order; Ch = 0	3; therapeutic relationship as client-therapist synchrony in vocal affectivity, emotion self-regulation [short-term psychodynamic therapy—0]	MATLAB	1; audio-transcripts, vocal arousal, self-report questionnaire; 1 [n = 30]
23	Peluso et al. (2012)	United States of America	1; stable attractors, emotion inertia, critical points, interpersonal influence based on emotional valence [Gottman’s differential equations model]; ODE, first-order; Ch = 0	3; therapeutic relationship as client-therapist affectivity interaction [gestalt therapy—0]	MATLAB	Only simulated data
24	Redington and Reidbord (1992)	United States of America	3; phase space reconstruction, flow of trajectories, detection of broad-band noise—power spectrum on Hz, fractal dimension [power spectrum analysis, autocorrelation analysis, fractal dimension]; NA; Ch = 1	1; physiological heart rate, cognitive mental stress [insight-oriented therapy conducted by a psychoanalyst—0]	LabVIEW 2, National Instruments Corp., Austin, TX (signal processing); Systat, Systat, Inc., Evanston, IL; DataDesk, Odesta Corp., Northbrook, IL (vizualization)	1; video-transcripts, heart rate physiology; 0 [n = 1]
25	Reidbord and Redington (1992)	United States of America	3; phase space reconstruction, flow of trajectories, detection of broad-band noise—power spectrum on Hz [power spectrum analysis, autocorrelation analysis]; NA; Ch = 1	1; physiological heart rate, cognitive mental stress [brief insight-oriented therapy conducted by a psychoanalyst—0]	SYST AT 5 (Systat); StatView II (Abacus Concepts); Odesta's DataDesk; LabVIEW 2; Mathematica (Wolfram Research); MathCad (MathSoft); Abacus Software's MacSpin	1; video-transcripts, heart rate physiology; 0 [n = 1]
26	Sabelli et al. (1990)	United States of America	3; state transitions—bipolarity [bifurcation model]; NA; Ch = 1	1; bipolar disorder, emotional states [psychotherapy + pharmacotherapy—0]	NA	2; self-report questionnaire; 0 [n = 3]
27	Schiepek et al. (2016a)	AUT/Germany	1; state dynamics, order transitions [dynamic complexity algorithm—fluctuation + distribution]; NA; Ch = 0.5	3; resilience or coping, autonomy, withdrawal, stress [integrated mainly systemic therapy—0]	Synergetic Navigation System (integrated analyses)	2; self-report questionnaire; 0 [n = 1]
28	Schiepek et al. (2014)	Austria	1; complexity, self-organization, local peaks of complexity, critical fluctuations, order transitions [dynamic complexity algorithm—fluctuation + distribution]; NA; Ch = 0.5	3; obsessive compulsive disorder, client’s cognitive-emotional dynamics [CBT—1]	Synergetic Navigation System (integrated analyses)	2, 3; self-report questionnaire; 0 [n = 23]
29	Schiepek et al. (2017)	Austria/Germany	3; synergetics core concepts—self-organized thresholds, synchronization patterns, phase transitions, chaotic dynamics [Schiepek’s differential equations model]; ODE, first-order; Ch = 1	3; client’s cognitive-emotional dynamics [general therapy—0]	MATLAB	Only simulated data
30	Schiepek et al. (2016b)	Austria/Germany	3; synergetics core concepts—self-organized thresholds, synchronization patterns, phase transitions, chaotic dynamics, dynamic patterns with and without the Verhulst-driven eigendynamics of the Emotions order parameter [Schiepek’s differential equations model, Verhulst-driven eigendynamics]; ODE, first-order; Ch = 1	3; client’s cognitive-emotional dynamics [general therapy—0]	MATLAB	2; self-report questionnaire; 0 [n = 1]
31	Schiepek et al. (1997)	Germany	3; topological complexity, chaoticity and sensitivity to initial conditions, nonperiodicity and nonpredictability of time-signal—correlation decay—detection of broad-band noise—power spectrum [sequential plan analysis, Fast Fourier Transformation on power spectra, autocorrelation analysis, determinism test, correlation dimension, largest Lyapunov exponents, local largest Lyapunov exponents]; NA; Ch = 1	2; therapeutic relationship as a client-therapist interaction of cognitive-emotional schemata—verbally and nonverbally communicated self-presentations [solution-oriented brief therapy—0]	NA	1; video-transcripts; 1 [n = 1]
32	Schiepek and Strunk (2010)	Austria	1; critical instability and fluctuations, phase transitions [dynamic complexity algorithm—fluctuation + distribution, permutation entropy, Lyapunov exponent]; NA; Ch = 1	3; obsessive compulsive disorder, client’s cognitive-emotional dynamics [general therapy—0]	NA	2, 3; self-report questionnaire; 0 [n1 = 94, n2 = 1]
33	Schiepek et al. (2013)	Austria	1; pattern complexity of signal, fluctuation —amplitude and frequency of changes in a signal— and distribution —scattering of values or system states within range of possible states, order transitions, critical instability [dynamic complexity algorithm—fluctuation + distribution]; NA; Ch = 0.5	3; obsessive compulsive disorder, client’s cognitive-emotional dynamics [CBT—0]	R, SPSS	2; self-report questionnaire; 0 [n = 18]
34	Schöller et al. (2018)	Austria/Germany	3; synergetics core concepts—self-organized thresholds, synchronization patterns, phase transitions, chaotic dynamics, critical instability [Schiepek’s differential equations model extended to control parameter dynamics]; ODE, first-order; Ch = 1	3; client’s cognitive-emotional dynamics, personality development [general therapy—0]	psysim.at web software	2; self-report questionnaire; 0 [n = 941]
35	Sharman (1998)	Canada	1; attractor states —repetitive defensive personality patterns—, repellor states —dissipating patterns—, state transitions and phase shifts, density of recurrence, anxiety as a control parameter [autocorrelation lag analysis, dynamic systems state-space model]; NA; Ch = 0	1; cognitive-affective personality components interactions controlled by anxiety levels [short-term psychodynamic therapy—0]	MacSHAPA program	1; video-transcripts; 0 [n = 1]
36	Stapelberg (2016)	Australia	2; spectral power density [Fast Fourier Transformation, autoregression analysis, detrended fluctuation analysis]; NA; Ch = 0	1; physiological heart rate variability, depression, anxiety [CBT—0]	MATLAB, SPSS	1; heart rate physiology, self-report questionnaire data; 0 [n = 88]
37	Tschacher and Haken (2019)	Switzerland	3; attractors, state evolution, entropy, potential function, degree of synchrony [Fokker-Planck equation]; PDE, second-order; Ch = 0	2; physiological nonverbal synchrony [general therapy—0]	MEA (motion energy analysis software)	1; heart rate physiology; 1 [n = 2]
38	Tschacher et al. (2015a)	Switzerland	3; order, invariant lagged relationships, phase space, attractor landscape, relaxation time to resettle after perturbation, damping influence [Landberger’s order, vector autoregression, Fokker-Planck equation]; PDE, second-order; Ch = 0	2; therapeutic relationship as client-therapist experiential, behavioral, and structural alliance [schema-centered therapy—0]	MEA (motion energy analysis software)	Only simulated data
39	Tschacher et al. (2015b)	Switzerland	3; pattern formation, phase transitions, stability and change [Fokker-Planck equation]; PDE, second-order; Ch = 0	2; therapeutic relationship as client-therapist experiential alliance—communion and agency –, or as behavioral alliance—nonverbal synchrony [person-centered Rogerian therapy—0]	MEA (motion energy analysis software)	1; video motion-energy-data; 1 [n = 1]
40	Tschacher et al. (1998)	Switzerland	1; order, self-organization, pattern formation [Landsberger’s order analysis, Shannon entropy]; NA; Ch = 0	3; therapeutic relationship as client-therapist alliance—progress within and outside of therapy setting [CBT, insight-oriented, client-centered, heuristic, schema therapy—0]	NA	3; self-report questionnaire; 0 [n = 28]
41	Walter et al. (2010)	Germany	1; topological complexity, unsteady development of changing complexity [dynamic complexity algorithm—fluctuation + distribution]; NA; Ch = 0.5	2; emotional abstraction patterns—relaxing, reflecting, experiencing, connecting [short-term solution-oriented therapy—0]	NA	1; video-transcripts; 0 [n = 1]

Note. (1b): country codes according to the affiliation of the first author; (2a): 1 = deterministic methods, 2 = stochastic methods, 3 = hybrid methods (a combination of deterministic and stochastic methods); (2b): list of DST/CT phenomena; (2c): list of DST/CT methods; (2d): ODE = ordinary differential equations, PDE = partial differential equations; (2e): order of differential equations; (2i): 0 = chaos not present, 0.5 = chaos theoretically, 1 = chaos present computationally; Hz = Hertz; (3a): 1 = the main phenomena are therapeutic outcomes (or semioutcomes in time-series sense)—focusing on the effect of therapy; 2 = the main phenomena are therapeutic processes—focusing on how the therapy develops regardless of the effectiveness of successful therapy; 3 = a combination of both process and outcome focuses; (3b): list of primary phenomena; (3d): list of psychotherapeutic intervention types—distinction between group = 1 and individual = 0 therapy; CBT = cognitive behavioral therapy; (4b): used software; (5b): 1 = micro (processes during therapy session, measured in seconds/minutes); 2 = meso (processes during daily life of patients, measured in days); 3 = macro (processes during therapy session, measured in weeks/sessions); (5a): list of empirical data types; (5c): 0 = individual data, 1 = dyadic data; (5d): clients’ sample size; NA = not available information.

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