Chaos Theory and Complexity Theory

2013 ◽  
Author(s):  
Keith Warren
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Systems Theory ◽  
Complexity Theory ◽  
Chaos Theory ◽  
Mathematical Framework ◽  
Nonlinear Interactions ◽  
Simple Systems ◽  
Over Time

Chaos theory and complexity theory, collectively known as nonlinear dynamics or dynamical systems theory, provide a mathematical framework for thinking about change over time. Chaos theory seeks an understanding of simple systems that may change in a sudden, unexpected, or irregular way. Complexity theory focuses on complex systems involving numerous interacting parts, which often give rise to unexpected order. The framework that encompasses both theories is one of nonlinear interactions between variables that give rise to outcomes that are not easily predictable. This entry provides a nonmathematical introduction, discussion of current research, and references for further reading.

scholarly journals Complexity Theory, Nonlinear Dynamics, and Change: Augmenting Systems Theory

10.18060/137 ◽  
2007 ◽  
Vol 8 (1) ◽  
pp. 141-151 ◽  
Author(s):  
Ralph Woehle
Keyword(s):  
Nonlinear Dynamics ◽  
Social Work ◽  
Difference Equation ◽  
Systems Theory ◽  
Complexity Theory ◽  
Change Processes ◽  
Edge Of Chaos ◽  
Good Measurement ◽  
Logistic Difference Equation ◽  
Over Time

Social work change processes are addressed in terms of complexity theory and nonlinear dynamics, adding the edge-of-chaos, as well as chaos to the entropy and homeostasis of ecosystems theory. Complexity theory sees the edge-of-chaos as valuable to living systems.A logistic difference equation is utilized to model the nonlinear dynamics of the hypothetical contentment of an individual. The modeling suggests that substantial input would be required to move an individual from homeostasis to the beneficial stage at the edge-of-chaos, but that too much input might result in chaos.With good measurement and data observed over time, social work might benefit from complexity theory and nonlinear dynamics, which are already advancing in related disciplines.

scholarly journals Theory of hybrid dynamical systems and its applications to biological and medical systems

2010 ◽  
Vol 368 (1930) ◽  
pp. 4893-4914 ◽  
Author(s):  
Kazuyuki Aihara ◽  
Hideyuki Suzuki
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Systems Theory ◽  
Control Systems ◽  
Hybrid Systems ◽  
Hybrid Dynamical Systems ◽  
Medical Systems ◽  
Theme Issue ◽  
And Control

In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on–off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.

Application of Nonlinear Dynamics Theory to Neuro-Occupation: A Case Study of Alcoholism

2007 ◽  
Vol 70 (8) ◽  
pp. 349-357 ◽  
Author(s):  
Emily Haltiwanger ◽  
Ivelisse Lazzarini ◽  
Homer Nazeran
Keyword(s):  
Social Sciences ◽  
Nonlinear Dynamics ◽  
Therapeutic Relationship ◽  
Chaos Theory ◽  
Single Case ◽  
Occupational Therapists ◽  
Single Case Study ◽  
Hidden Order ◽  
Over Time

Nonlinear dynamics systems theory, also referred to as chaos theory, is infiltrating the biomedical and social sciences, including the practice of occupational therapy. Consequently, the Neuro-occupation model has emerged for the treatment of different illnesses, in which a therapist strives to apply the benefits of this theory. This model provides occupational therapists with a method of anticipating the natural flux between underlying or hidden order and chaos in occupations, which allows individuals to function at their highest level. These occupations typically involve the interaction of numerous variables over time. By considering a nonlinear dynamics approach in illnesses such as alcoholism, occupational therapists may understand how meaningful occupations serve as a catalyst to facilitate change, which may assist in better understanding the effect of the therapeutic relationship with the clients they serve. This paper explains the nonlinear dynamics of the interventions in a single case study on alcoholism using the Neuro-occupation model.

scholarly journals Walking droplets through the lens of dynamical systems

2020 ◽  
Vol 34 (34) ◽  
pp. 2030009
Author(s):  
Aminur Rahman ◽  
Denis Blackmore
Keyword(s):  
Nonlinear Dynamics ◽  
Quantum Mechanics ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Systems Analysis ◽  
Research Field ◽  
Physical Models ◽  
The Past ◽  
Dynamical Systems Analysis ◽  
History Of

Over the past decade the study of fluidic droplets bouncing and skipping (or “walking”) on a vibrating fluid bath has gone from an interesting experiment to a vibrant research field. The field exhibits challenging fluids problems, potential connections with quantum mechanics, and complex nonlinear dynamics. We detail advancements in the field of walking droplets through the lens of Dynamical Systems Theory, and outline questions that can be answered using dynamical systems analysis. The paper begins by discussing the history of the fluidic experiments and their resemblance to quantum experiments. With this physics backdrop, we paint a portrait of the complex nonlinear dynamics present in physical models of various walking droplet systems. Naturally, these investigations lead to even more questions, and some unsolved problems that are bound to benefit from rigorous Dynamical Systems Analysis are outlined.

Implications of chaos theory for engineering science

1997 ◽  
Vol 211 (5) ◽  
pp. 349-363 ◽  
Author(s):  
G Baker ◽  
F A McRobie ◽  
J M T Thompson
Keyword(s):  
Dynamical Systems ◽  
Systems Theory ◽  
Chaos Theory ◽  
Chemical Engineering ◽  
Dynamical Systems Theory ◽  
Engineering Science ◽  
Linear Dynamical Systems ◽  
Non Linear

A review is presented of the applications of non-linear dynamical systems theory (or chaos theory) in mechanical, civil, electrical and chemical engineering

scholarly journals Osteopathy in the Cranial Field from a Systems Theory Perspective

2021 ◽  
Vol 7 (5) ◽  
pp. 1-9
Author(s):  
Rene J Zweedijk ◽  
Keyword(s):  
Artificial Intelligence ◽  
Complex Systems ◽  
Systems Theory ◽  
Systems Thinking ◽  
Chaos Theory ◽  
Future Research ◽  
Essential Value ◽  
Complex Systems Thinking ◽  
Scientific Substantiation

A proposition is made for scientific substantiation of “Primary respiration” and related concepts, including suggestions for future research. For research and support, the field of mathematics, artificial intelligence, chaos theory and complex systems thinking can be of fundamental and essential value.

scholarly journals Inojezični razvoj i teorije dinamičnih sustava

2018 ◽  
Vol 13 (2) ◽  
pp. 287
Author(s):  
Marijana Bašić
Keyword(s):  
System Theory ◽  
Complex Systems ◽  
Systems Theory ◽  
Complexity Theory ◽  
Dynamic Systems ◽  
Adaptive System ◽  
Complex Adaptive System ◽  
Dynamic Systems Theory ◽  
Complex Adaptive

U ovome se radu raspravlja o dosadašnjim teorijskim spoznajama o inojezičnome razvoju iz perspektive teorije dinamičnih sustava (engl. Dynamic systems theory, tj. DST), o pokušaju oblikovanja razvojnoga indeksa, o pojavi teorijskoga pluralizma u okviru kojega se ukazalo na sličnosti između složenih nepravocrtnih sustava koji se pojavljuju u prirodi i pri ovladavanju inim jezikom te o različitim načinima mjerenja složenosti, točnosti i tečnosti, tj. STOT-a (engl. complexity, accuracy and fluency, tj. CAF). Opisuju se nove metode istraživanja inojezičnoga razvoja te daje detaljan pregled najvažnijih recentnih istraživanja u okviru teorije dinamičnih sustava, odnosno teorije kaosa ili složenosti (engl. Chaos/complexity theory, tj. C/ CT), teorije složenih prilagodljivih sustava (engl. Complex adaptive system theory, tj. CAS) i (nad)teorije složenih sustava (engl. Complex systems supra-theory).

scholarly journals A New Perspective: The Implication of Chaos/Complexity Theory in Language through Dichotomies

2020 ◽  
Vol 1 (3) ◽  
pp. 372-377
Author(s):  
Zahra Jafari ◽  
Ashraf Maibodi ◽  
Muhammad Natsir
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamical System ◽  
System Theory ◽  
Second Language Acquisition ◽  
Language Acquisition ◽  
Complexity Theory ◽  
Dynamical System Theory ◽  
Points Of View ◽  
New Perspective ◽  
Over Time

This study opens different points of view at chaos/complexity theory (C/CT) which is still a new theory in second language acquisition. Pro. Larsen-Freeman and her colleagues considered a variety of characteristics, C/CT is known as nonlinear dynamics or dynamical system theory that provides a framework for thinking about change over time. Scientists claim that one can see not only the laws of chaos but also those of order, through which a strong explanation for how any collection of components will organize itself and it can be generated in dichotomies. They attempt to rationalize the behavior of large and complex systems, believing they cannot be explained by usual rules of nature

Complex Systems

2020 ◽  
pp. 209-220
Author(s):  
Stephen K. Reed
Keyword(s):  
Coral Reef ◽  
Dynamical Systems ◽  
Complex Systems ◽  
Computer Science ◽  
Slow Rate ◽  
Earth Science ◽  
Critical Transitions ◽  
Rate Of Recovery ◽  
Over Time ◽  
Sudden Collapse

Dynamical systems are complex systems that fluctuate over time. Sudden transitions occur after reaching a tipping point that can have detrimental consequences, such as the sudden collapse of a coral reef. A slow rate of recovery from smaller challenges can serve as a warning for critical transitions. The increasing importance of complex systems for understanding science requires excellent instruction. NetLogo modules offer one approach for learning about emergent interactions. A review of instruction distinguished between the teaching of complex systems in biology, chemistry, computer science, earth science, ecology, physics, and engineering. Most instruction has focused on the domains of biology and ecology although there is a need to extend coverage to other topics. There is also need for more research on effective teaching because instruction on complex systems is still in its infancy.

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