scholarly journals Assessing the continuum between temperament and affective illness: psychiatric and mathematical perspectives

2018 ◽  
Vol 373 (1744) ◽  
pp. 20170168 ◽  
Author(s):  
William Sulis
Keyword(s):  
Mental Illness ◽  
Affective Disorders ◽  
Nonlinear Dynamical Systems ◽  
Mental Illnesses ◽  
Mathematical Methods ◽  
Theme Issue ◽  
Nonlinear Dynamical ◽  
Alternative Approach ◽  
Long Time ◽  
The Continuum

Temperament of healthy people and mental illnesses, particularly affective disorders, have been conjectured to lie along a continuum of neurobehavioural regulation. Understanding the nature of this continuum may better inform the construction of taxonomies for both categories of behaviour. Both temperament and mental illness refer to patterns of behaviour that manifest over long time scales (weeks to years) and they appear to share many underlying neuroregulatory systems. This continuum is discussed from the perspectives of nonlinear dynamical systems theory, neurobiology and psychiatry as applied to understanding such multiscale time-series behaviour. Particular emphasis is given to issues of generativity, fungibility, metastability, non-stationarity and contextuality. Implications of these dynamical properties for the development of taxonomies will be discussed. Problems with the over-reliance of psychologists on statistical and mathematical methods in deriving their taxonomies (particularly those based on factor analysis) will be discussed from a dynamical perspective. An alternative approach to temperament based upon functionality, and its discriminative capabilities in mental illness, is presented. This article is part of the theme issue ‘Diverse perspectives on diversity: multi-disciplinary approaches to taxonomies of individual differences’.

Sparse Recovery and Dictionary Learning to Identify the Nonlinear Dynamical Systems: One Step Toward Finding Bifurcation Points in Real Systems

2019 ◽  
Vol 29 (03) ◽  
pp. 1950030 ◽  
Author(s):  
Fahimeh Nazarimehr ◽  
Aboozar Ghaffari ◽  
Sajad Jafari ◽  
Seyed Mohammad Reza Hashemi Golpayegani
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Dictionary Learning ◽  
Nonlinear Dynamical Systems ◽  
Sparse Recovery ◽  
Governing Equations ◽  
Nonlinear Dynamical ◽  
Bifurcation Points ◽  
Long Time

Modeling real dynamical systems is an important challenge in many areas of science. Extracting governing equations of systems from their time-series is a possible solution for such a challenge. In this paper, we use the sparse recovery and dictionary learning to extract governing equations of a system with parametric basis functions. In this algorithm, the assumption of sparsity in the functions of dynamical equations is used. The proposed algorithm is applied to different types of discrete and continuous nonlinear dynamical systems to show the generalization ability of this method. On the other hand, transition from one dynamical regime to another is an important concept in studying real world complex systems like biological and climate systems. Lyapunov exponent is an early warning index. It can predict bifurcation points in dynamical systems. Computation of Lyapunov exponent is a major challenge in its application in real systems, since it needs long time data to be accurate. In this paper, we use the predicted governing equation to generate long time-series, which is needed for Lyapunov exponent calculation. So the proposed method can help us to predict bifurcation points by accurate calculation of Lyapunov exponents.

scholarly journals Tracking Nonlinear Oscillations with Time-Delayed Feedback

2006 ◽  
Vol 5-6 ◽  
pp. 417-424
Author(s):  
Jan Sieber ◽  
B. Krauskopf
Keyword(s):  
Dynamical System ◽  
Hopf Bifurcation ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Oscillations ◽  
Stability Boundary ◽  
Nonlinear Dynamical ◽  
Friction Oscillator ◽  
Long Time ◽  
Basic Ideas ◽  
The Stability

We demonstrate a method for tracking the onset of oscillations (Hopf bifurcation) in nonlinear dynamical systems. Our method does not require a mathematical model of the dynamical system but instead relies on feedback controllability. This makes the approach potentially applicable in an experiment. The main advantage of our method is that it allows one to vary parameters directly along the stability boundary. In other words, there is no need to observe the transient oscillations of the dynamical system for a long time to determine their decay or growth. Moreover, the procedure automatically tracks the change of the critical frequency along the boundary and is able to continue the Hopf bifurcation curve into parameter regions where other modes are unstable.We illustrate the basic ideas with a numerical realization of the classical autonomous dry friction oscillator.

Puerperal Mental Illness, Clinical Features and Classification: A Study of 142 Mother-and-Baby Admissions

1985 ◽  
Vol 147 (6) ◽  
pp. 647-654 ◽  
Author(s):  
E. S. Meitzer ◽  
R. Kumar
Keyword(s):  
Mental Illness ◽  
Clinical Features ◽  
Affective Disorders ◽  
Psychiatric Hospitals ◽  
Mental Illnesses ◽  
The South ◽  
Considerable Uncertainty ◽  
Patient Sample ◽  
Department Of Health ◽  
Provision Of Services

The case notes were studied of 142 mothers admitted to psychiatric hospitals in the south-east Thames region within 12 months of childbirth during the years 1979 and 1980. Only 6% of the sample were categorised as schizophrenics by RDC criteria, whereas affective disorders were found to predominate in 80%. Manic and schizo-affective illnesses almost always began within two weeks of parturition, as did psychotic depressions. A third of the patient sample had suffered relatively minor disorders, and given adequate resources, some might have been better managed in the community. A parallel investigation of diagnostic returns to the Department of Health revealed considerable uncertainty about how to classify puerperal mental illnesses in accordance with ICD-9. There is an urgent need to improve the system for categorising and registering mental illnesses related to childbirth. Until this is achieved, research into aetiology, outcome, and the provision of services will continue to be impeded.

VISUALIZING BIFURCATIONS IN HIGH DIMENSIONAL SYSTEMS: THE SPECTRAL BIFURCATION DIAGRAM

2003 ◽  
Vol 13 (10) ◽  
pp. 3015-3027 ◽  
Author(s):  
DAVID ORRELL ◽  
LEONARD A. SMITH
Keyword(s):  
Control Parameter ◽  
Nonlinear Dynamical Systems ◽  
The Other ◽  
High Dimensional ◽  
Behavior Changes ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Third ◽  
Alternative Approach ◽  
Lorenz 96

This paper presents methods to visualize bifurcations in flows of nonlinear dynamical systems, using the Lorenz '96 systems as examples. Three techniques are considered; the first two, density and max/min diagrams, are analagous to the bifurcation diagrams used for maps, which indicate how the system's behavior changes with a control parameter. However the diagrams are generally harder to interpret than the corresponding diagrams of maps, due to the continuous nature of the flow. The third technique takes an alternative approach: by calculating the power spectrum at each value of the control parameter, a plot is produced which clearly shows the changes between periodic, quasi-periodic, and chaotic states, and reveals structure not shown by the other methods.

scholarly journals Semigroup applications everywhere

2020 ◽  
Vol 378 (2185) ◽  
pp. 20190610
Author(s):  
Rainer Nagel ◽  
Abdelaziz Rhandi
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Volterra Equations ◽  
Special Issue ◽  
Theme Issue ◽  
Nonlinear Dynamical ◽  
Qualitative And Quantitative ◽  
Abstract Evolution Equation ◽  
Quantitative Properties ◽  
Functional Differential

Most dynamical systems arise from partial differential equations (PDEs) that can be represented as an abstract evolution equation on a suitable state space complemented by an initial or final condition. Thus, the system can be written as a Cauchy problem on an abstract function space with appropriate topological structures. To study the qualitative and quantitative properties of the solutions, the theory of one-parameter operator semigroups is a most powerful tool. This approach has been used by many authors and applied to quite different fields, e.g. ordinary and PDEs, nonlinear dynamical systems, control theory, functional differential and Volterra equations, mathematical physics, mathematical biology, stochastic processes. The present special issue of Philosophical Transactions includes papers on semigroups and their applications. This article is part of the theme issue ‘Semigroup applications everywhere’.

Nonlinear Dynamical Systems

1985 ◽  
Vol 38 (10) ◽  
pp. 1284-1286 ◽  
Author(s):  
F. C. Moon
Keyword(s):  
Dynamical Systems ◽  
Solid Mechanics ◽  
Nonlinear Dynamical Systems ◽  
Fractal Dimensions ◽  
Nonlinear Problems ◽  
Nonlinear Dynamical ◽  
Time Dynamic ◽  
Long Time ◽  
New Ideas ◽  
Initial Starting

New discoveries have been made recently about the nature of complex motions in nonlinear dynamics. These new concepts are changing many of the ideas about dynamical systems in physics and in particular fluid and solid mechanics. One new phenomenon is the apparently random or chaotic output of deterministic systems with no random inputs. Another is the sensitivity of the long time dynamic history of many systems to initial starting conditions even when the motion is not chaotic. New mathematical ideas to describe this phenomenon are entering the field of nonlinear vibrations and include ideas from topology and analysis such as Poincare´ maps, fractal dimensions, Cantor sets and strange attractors. These new ideas are already making their way into the engineering vibrations laboratory. Further research in this field is needed to extend these new ideas to multi-degree of freedom and continuum vibration problems. Also the loss of predictability in certain nonlinear problems should be studied for its impact on the field of numerical simulation in mechanics of nonlinear materials and structures.

scholarly journals Evaluating the talking cure

2020 ◽  
Author(s):  
Megha Verma
Keyword(s):  
Mental Illness ◽  
Controlled Trial ◽  
Mental Illnesses ◽  
Behaviour Therapy ◽  
Philosophical Foundations ◽  
Cognitive Behaviour ◽  
Long Time ◽  
Complex Solutions ◽  
Mental Illness Treatment ◽  
Talking Cure

It would seem that a disorder as complex as a mental illness would require equally complex solutions. “Talking cures”, known today as psychotherapies, were lauded as unscientific for a very long time.1 Today, cognitive behaviour therapy (CBT) is a psychotherapeutic technique that has shown considerable success in improving the prognosis for many mental illnesses using the scientific method. It is considered a panacea by some for mental illness amidst the zeitgeist of skepticism for pharmacology. This article explores the philosophical foundations of CBT and explains how a technique considered as unscientific is now the gold-standard in mental illness treatment. A randomized controlled trial (RCT) will also be discussed to examine its validity on psychotherapy and determine whether efficiency studies may be more suitable to adequately compare psychotherapies.

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