Application of Chaos Research Papers (original) (raw)

В данной работе делается попытка показать, с помощью методов математического моделирования, при каких условиях процессы самоорганизации в рабочей среде могут приводить к взрывному характеру конфликтов, к нелинейным эффектам в их развитии в силу действия внутренних факторов. Первый раздел статьи включает краткое рассмотрение роли внешних и внутренних факторов в развитии волн стачечной динамики. Во втором разделе предлагается нелинейная модель стачечной динамики, проводится ее анализ; в частности, выявляются условия, в которых эта динамика может иметь неустойчивый, хаотический характер, когда малые (возможно, случайные) воздействия приводят к резким изменениям стачечной активности. Именно такие процессы изучает синергетика.
In this paper an attempt is made to show by means of mathematical modeling, the conditions under which self-organization processes in the working environment can lead to explosive nature of the conflict, to nonlinear effects in their development by virtue of endogeneous and exogeneous factors. The first section of the article includes a brief review of the role of external and internal factors in the development of the strike wave dynamics. The second section provides a non-linear model of the strike dynamics and its analysis; in particular, identifies the conditions under which these dynamics can be unstable or chaotic, when small (possibly random) effects lead to rapid changes in strike activity. It is these processes synergetics studies.

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- Labour history, Nonlinear dynamics, Social History, Mathematical Modelling

Синергетику часто называют наукой о сложном, учением о самоорганизации, об универсальных закономерностях эволюции сложных динамических систем, претерпевающих резкие изменения состояний в периоды нестабильности. Центральный вопрос, который обсуждается историками в этой связи – влияние случайностей, которые принципиально невозможно предугадать и прогнозировать, на общий характер развития изучаемого процесса. С этим вопросом связаны и новые подходы к изучению альтернатив общественного развития, возникающих в точках бифуркации.
Методология синергетики может дать ключ к пониманию резких изменений в динамике процесса, которые могут происходить и без сколько-нибудь заметных внешних причин, в силу нелинейного его характера.
Цель данной работы -¬ обсуждение методологических проблем применения концепций синергетики в исторических исследованиях.

In this paper, we will study dynamics of an important physiological control system—human gait in disease and aging. The investigation of fluctuations overlying periodic motion in human walking may provide valuable information about neuromuscular system generating both normal and pathological walking patterns. Using nonlinear dynamics analysis, we analyzed walking gaits of the young, elderly and aged subjects with Parkinson’s disease. This inquiry demonstrates that nonlinear time-series analysis methods based on time-delay embedding may provide useful insight into the neuromuscular control of human locomotion.

- by Sajid Iqbal
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- Dynamical Systems, Mathematical Biology, Chaos Theory, Mathematical Modelling

Chaos is an ontological and aesthetic category in the works of Howard Phillips Lovecraft. This category serves as the basis of cosmocentrism in his works. Chaos category is one of the sources of his inspiration. It expresses views on the essence of human existence, psychology and ethics of characters in his works. This is expressed not only in anthropomorphic and cosmogonic artistic images, but also in the frankly anti-anthropocentric views of the author in which a person is only a doll in the boundless space of the Divine Theater of the Absurd. Meeting of heroes with death is just another metamorphosis on the path to constant change and madness.
Thіs article is devoted to the interpretation of the Chaos mythologem in relation to artistic images in H.P. Lovecraft’s works which as well as the Chaos mythologem remain scarcely explored in modern Ukrainian aesthetics. In the writer’s works, the meaning of the Chaos symbolism is closely linked to the natural and cosmic unidentified and mysterious elements that the author considered to be the beginning of everything.

- by Андрій Волинець
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- Application of Chaos, H.P. Lovecraft, Chaos, Mithology

IT'S HERE NOW!!! IT’S GOING TO BE REAL STRANGE. PEOPLE MUST NOT BE AFRAID, IN FACT, ALL PEOPLE NEED TO BE REAL HAPPY ABOUT THIS EVENT AND BE READY TO GET OUTSIDE. GROUNDED. THIS IS MEANT TO CLEAN ALL OF THE POLLUTION AND PROBABLY EVEN... more

- by MIKE EMERY
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- History, Ancient History, Physiology, Sociology

This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of determin‐ istic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.

- by Sajid Iqbal
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- Fractal Geometry, Mobile Robotics, Mathematical Biology, Swarm Intelligence

—Everything in this universe is, to some extent, nonlinear in nature. For certain parameter values, a nonlinear dynamical system exhibits erratic behavior called chaos. In this paper, a novel yet simple method is presented for implementing nonlinear systems using operational amplifiers (op-amps) based circuits like integrators and subtractors. The non-linear function sin 2 (x) has been written in terms of polynomial equation using Taylor series expansion and that polynomial equation has been implemented using op-amps. The transition to chaos has been observed by varying the control parameters in simulations and in experiments.

- by Sajid Iqbal
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- Robotics, Humanoid Robotics, Nonlinear dynamics, Chaos Theory

Recognizing and taking into consideration multiple forms of disorder constitutes a privileged way to grasp what is at the core of the idea of complexity. From physics and biology to psychology, sociology and anthropology, it seems legitimate to question the role of disorder in the everyday life. Considering phenomena such as chance, hazard, agitation, dispersion, perturbation, accident, noise, error, it seems therefore critical for practitioners and researchers in education to focus their attention on complementary, antagonistic and concurring relationships between order and disorder, and to question the role they play in the processes through which education and learning self-organize themselves. Disorder appears therefore as a key concept that has to be considered in education, in conjunction with the ideas of order, interaction and organization.
Promoting a conception of education that acknowledges and embraces the role played by heterogeneous forms of disorder appears therefore as a critical project. It raises at least three questions, respectively from an epistemological, educational and ethical perspective.

- by Michel Alhadeff-Jones
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- Education, Philosophy of Education, Complexity Theory, Nonlinear dynamics

DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.

- by Sajid Iqbal and +1
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- Power Electronics, Mathematical Biology, Chaos Theory, Mathematical Modelling

In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of 4-D chaotic systems, viz. identical Lorenz-Stenflo(LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non-identical LS and Qi systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical LS and Qi systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the identical and non-identical, uncertain LS and Qi 4-D chaotic systems.

- by Lucas Máximo Alves
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- Mathematical Biology, Chaos Theory, Mathematical Modelling, Chaos (Physics)

A new four-dimensional, hyperchaotic dynamic system, based on Lorenz dynamics, is presented. Besides, the most representative dynamics which may be found in this new system are located in the phase space and are analyzed here. The new system is especially designed to improve the complexity of Lorenz dynamics, which, despite being a paradigm to understand the chaotic dissipative flows, is a very simple example and shows great vulnerability when used in secure communications. Here, we demonstrate the vulnerability of the Lorenz system in a general way. The proposed 4D system increases the complexity of the Lorenz dynamics. The trajectories of the novel system include structures going from chaos to hyperchaos and chaotic-transient solutions. The symmetry and the stability of the proposed system are also studied. First return maps, Poincaré sections, and bifurcation diagrams allow characterizing the global system behavior and locating some coexisting structures. Numerical results about the first return maps, Poincaré cross sections, Lyapunov spectrum, and Kaplan-Yorke dimension demonstrate the complexity of the proposed equations.

- by Maria Pilar Mareca and +1
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- Molecular Physics, Quantum Chemistry, Molecular Dynamics Simulation, Mathematical Biology

This paper presents the new Lorenz unlike chaotic attractor which is constructed by a three non linear first order differential equations. These equations are arranged in a three dimensional autonomous systems. The dynamic behavior of the new chaotic system is shown such as time series, strange attractors, and bifurcations. Numerical experience also shows that when the parameter 'd' is varied, the global non linear amplitude is also varying. The paper ends with some possible research and development recommendations.

- by Richard Ottermanns
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- Resilience, Ecology, Dynamical systems and Chaos, Application of Chaos

"-Abstract-
Organizations are built up with the assumption of existing forever. This foundational premise brings the idea of control and order, particularly with the narrative of management. Hence, management is presented as a panacea of all external and internal chaotic problems as a sort of utopian ideal and narrative in order to provide order and development. This supposedly reality based utopian fiction of orderly organization cause a dream-like state that misses the continuous flux of the reality. Hence, in this study, we use dystopia as a base in order to catch the reality of chaos and the narrative of inherent entropy of organizations. Depending upon discussions on science fiction in popular culture products and their reflections in the organization studies, we argue that, the chaotic depiction of future provides a metaphorical narrative. Particularly, by taking Warhammer Universe as a dystopian case, we demonstrate that the inherent entropy of organizations is a vital part of their existence, not just a mere annoyance that can simply be dealt with."

This article proposes an approach to synchronize a class of unidimensional spatiotemporal chaotic systems using exponential nonlinear observers. The article focuses on generalized synchronization with parameter mismatching and a unidirectional master–slave topology. The approach involves the conception of two different nonlinear observers to estimate the unknown parameters of a master system, such that the estimated parameters can be injected into a controller to synchronize the slave with the master. To illustrate the proposed approach, an example based on the Gray–Scott equations that exposes the synchronization and the observer conception is presented.

Everything in this universe is, to some extent, nonlinear in nature. For certain parameter values, a nonlinear dynamical system exhibits erratic behavior called chaos. In this paper, a novel yet simple method is presented for implementing nonlinear systems using operational amplifiers (op-amps) based circuits like integrators and subtractors. The non-linear function sin2 (x) has been written in terms of polynomial equation using Taylor series expansion and that polynomial equation has been implemented using op-amps. The transition to chaos has been observed by varying the control parameters in simulations and in experiments.

Many research groups developed bifurcation diagrams, Poincare maps and computed Feigenbaum constants for passive walkers. Very few attempts have been made for performing nonlinear time-series analyses of these complex dynamical systems. Besides, Garcia’s et al.’s the simplest walking model, the compass-gait biped model is the most commonly used passive dynamic walking (PDW) biped robot by the biomechanists, robotics engineers and chaos theorists. We accomplished nonlinear analysis of a time-series generated by the compass-gait biped and aimed to examine its dynamical behavior. The walking gait time-series data presented chaotic dynamics as fractal dimensions and positive Lyapunov exponents were found.

- by Sajid Iqbal
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- Autonomous Robotics, Humanoid Robotics, Chaos Theory, Educational Robotics

This article presents a summary of applications of chaos and fractals in robotics. Firstly, basic concepts of deterministic chaos and fractals are discussed. Then, fundamental tools of chaos theory used for identifying and quantifying chaotic dynamics will be shared. Principal applications of chaos and fractal structures in robotics research, such as chaotic mobile robots, chaotic behaviour exhibited by mobile robots interacting with the environment, chaotic optimization algorithms, chaotic dynamics in bipedal locomotion and fractal mechanisms in modular robots will be presented. A brief survey is reported and an analysis of the reviewed publications is also presented.

- by Sajid Iqbal
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- Engineering, Fractal Geometry, Chaos Theory, Locomotion

- by LIZETH TORRES and +1
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- Mathematical Biology, Chaos Theory, Synchronization, Mathematical Modelling

This paper deals with nonlinear dynamics of a PWM current-programmed H-Bridge. Fully chaotic behaviours appear and disappear under control tuning of the current loop. To explain how this strange dynamics evolve, we present a model that is a parametric one-dimensional piecewise linear map. We show how to apply a recent advance in chaos theory in order to determine the fixed points analytically, their domains of stability, and of the bifurcation points. Bifurcations which are nongeneric for smooth dynamical systems, also called Border Collision Bifurcations, allow a better understanding of the bifurcation diagram. With this example, we show that it is possible to predict the appearance of chaos in this converter in an entirely analytical way.

- by Martina Roß-Nickoll
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- Resilience, Nonlinear dynamics, Ecology, Population Dynamics

- by Sajid Iqbal
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- Robotics, Robotics (Computer Science), Mobile Robotics, Autonomous Robotics