Period-2 Cycles and 2:1 Phase Locking in a Biological Clock Driven by Temperature Pulses

Hütt, Marc‐Thorsten; Rascher, Uwe; Beck, F.; Lüttge, Ulrich

doi:10.1006/jtbi.2002.3031

Cited by 10 publications

(4 citation statements)

References 12 publications

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“…It is well-known that such periodic driving can trigger a complex dynamical response (e.g., Glass, 2001, for a general discussion and Hütt et al, 2002, for an empirical example of a temperature-driven photosynthetic activity of a plant leaf). While we believe that the psychotherapy itself is not affected by such a driver, the dynamical variables extracted by the TPQ certainly may justify our choice of a discrete-time model.…”

Section: Discussionmentioning

confidence: 99%

Psychotherapy Is Chaotic—(Not Only) in a Computational World

et al. 2017

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Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes.Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams.Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes.Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy.

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Section: Discussionmentioning

confidence: 99%

Psychotherapy Is Chaotic—(Not Only) in a Computational World

et al. 2017

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“…In this sense, the measurement process, induced by the TPQ, forms these variables at discrete times and the psychotherapy dynamics as a system is periodically driven by the TPQ. It is well-known that such periodic driving can trigger a complex dynamical response (Glass 2001 ; Hütt 2001 ; Hütt et al 2002 ).…”

Section: Discussionmentioning

confidence: 99%

Personality development in psychotherapy: a synergetic model of state-trait dynamics

et al. 2018

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Theoretical models of psychotherapy not only try to predict outcome but also intend to explain patterns of change. Studies showed that psychotherapeutic change processes are characterized by nonlinearity, complexity, and discontinuous transitions. By this, theoretical models of psychotherapy should be able to reproduce these dynamic features. Using time series derived from daily measures through internet-based real-time monitoring as empirical reference, we earlier presented a model of psychotherapy which includes five state variables and four trait variables. In mathematical terms, the traits modulate the shape of the functions which define the nonlinear interactions between the variables (states) of the model. The functions are integrated into five coupled nonlinear difference equations. In the present paper, we model how traits (dispositions or competencies of a person) can continuously be altered by new experiences and states (cognition, emotion, behavior). Adding equations that link states to traits, this model not only describes how therapeutic interventions modulate short-term change and fluctuations of psychological states, but also how these can influence traits. Speaking in terms of Synergetics (theory of self-organization in complex systems), the states correspond to the order parameters and the traits to the control parameters of the system. In terms of psychology, trait dynamics is driven by the states—i.e., by the concrete experiences of a client—and creates a process of personality development at a slower time scale than that of the state dynamics (separation of time scales between control and order parameter dynamics).

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“…As another manifestation of robustness, this phase-locking may persist even in the presence of stochastic noise [42][43][44]. Entrainment may also occur with respect to temperature, especially in plants [45,46]. The clock is a very complex system, involving transcriptional/translational feedback and influencing cellular functions from development to metabolism.…”

Section: Cellular Rhythmsmentioning

confidence: 96%

Models of cell signaling pathways

Bhalla

2004

Current Opinion in Genetics & Development

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Period-2 Cycles and 2:1 Phase Locking in a Biological Clock Driven by Temperature Pulses

Cited by 10 publications

References 12 publications

Psychotherapy Is Chaotic—(Not Only) in a Computational World

Psychotherapy Is Chaotic—(Not Only) in a Computational World

Personality development in psychotherapy: a synergetic model of state-trait dynamics

Models of cell signaling pathways

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