MATHEMATICAL MODEL OF ARCHITECTURE AND LEARNING PROCESSES OF ARTIFICIAL NEURAL NETWORKS by ANDRZEJ BIELECKI

“… A mathematical model of architecture and learning processes of multilayer artificial neural netwoks is discussed in the paper. Dynamical systems theory is used to describe the learning precess of networks consisting of linear, weakly nonlinear and nonlinear neurons. …”
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DYNAMIC SYSTEMS by Dragos Vasile VÎGA, Olimpia PECINGINA, Constantin BOGDAN

“…This article introduces concepts of dynamical systems theory such as phase space, phase space reconstruction and analysis of phase space, and their application to theanalysis of behaving agents.…”
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Nonlinear dynamics in psychology by Stephen J. Guastello

“…This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. …”
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Extracting Qualitative Dynamics from Numerical Experiments by Yip, Kenneth Man-Kam

“…This paper presents an approach for the automatic reconstruction of the full dynamical behavior from the numerical results by exploiting knowledge of Dynamical Systems Theory and techniques from computational geometry and computer vision. …”
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The Bifurcation Interpreter: A Step Towards the Automatic Analysis of Dynamical Systems by Abelson, Harold

“…The Interpreter incorporates knowledge about dynamical systems theory, which it uses to guide the simulations, to interpret the results, and to minimize the effects of numerical error.…”
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Modal science by Williamson, T

“…In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal logic. …”

Dynamics of a Four-Dimensional Economic Model by Gheorghe Moza, Oana Brandibur, Ariana Găină

“…By a qualitative analysis based on tools from dynamical systems theory, we obtain in the new model that the three economic indicators can be stabilized to three equilibrium states.…”
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Dynamic parameters for Brazilian financial time series by Gerson Francisco, Cláudio Paiva, Rogerio Rosenfeld

“… In this study we analyse a Brazilian stock index called IBOVESPA using techniques from dynamical systems theory and stochastic processes. We discuss the Lyapunov exponent, the correlation dimension, the LempelZiv complexity, the Hurst exponent and the BDS statistics. …”
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Morpho-elastodynamics: the long-time dynamics of elastic growth. by Vandiver, R, Goriely, A

“…These evolution laws lead to new dynamical systems that can be studied by the classical methods of dynamical systems theory.…”

BIFURCATION-ANALYSIS OF THE CONTROL OF AN ADAPTIVE EQUALIZER by Moroz, I, Baigent, S, Clayton, F, Lever, K

“…Techniques from dynamical systems theory are used to analyse the model, and show that with sensible choices of physical parameters, there is no possibility of periodic behaviour. © 1992 The Royal Society.…”

Codimension one and two bifurcations in Cattaneo-Christov heat flux model by Wei, Z, Zhang, W, Moroz, I, Kuznetsov, NV

“…Here we return to that paper and use techniques from dynamical systems theory to analyse the codimension-one Hopf bifurcation and codimension-two double-zero Bogdanov-Takens bifurcation. …”

Bi-stable dynamics of a host-pathogen model by Roumen Anguelov, Rebecca Bekker, Yves Dumont

“…To investigate the long term behavior, we use LaSalle Invariance Principle to derive sufficient conditions for global asymptotic stability of the pathogen free equilibrium and monotone dynamical systems theory to provide sufficient conditions for permanence of the system. …”
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Transient resetting: a novel mechanism for synchrony and its biological examples. by Chunguang Li, Luonan Chen, Kazuyuki Aihara

“…In this paper, by using simple dynamical systems theory, we present a novel mechanism, named transient resetting, for the synchronization of uncoupled biological oscillators with stimuli. …”
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Convergence and periodicity in a delayed network of neurons with threshold nonlinearity by Shangjiang Guo, Lihong Huang, Jianhong Wu

“…The discontinuity of the signal transmission functions, however, makes it difficult to apply the existing dynamical systems theory which usually requires continuity and smoothness. …”
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Auto-organização e complexidade: o problema do desenvolvimento do ciclo vigília-sono by José Roberto Castilho Piqueira, Ana Amélia Benedito-Silva

“…<br>THIS ARTICLE is a trial on stablishing some theoretical formalisms for the concepts of self-organizing and complex biological systems, using ideas from Information Theory and Dynamical Systems Theory. As an example the organization of the sleep-wake cycle in babies is studied, applying the methods proposed.…”
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New geography-mathematic approaches in the tasks of design of distribution of harmful admixtures in an atmosphere by Yu.Ya. Bunyakova

“…It is presented a qualitative overview of the new conceptual approaches, which are based on the provisions of the chaos theory, dynamical systems theory, fractal geometry, analysis of  Lyapunov exponents, and others, to problems of modeling the propagation of pollution impurities in the atmosphere of industrial cities and predicting the evolutionary dynamics. …”
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Reconceiving Cybernetics in Light of Thomistic Realism by John T. Laracy, Fr. Joseph R. Laracy

“…Since its origins in the early twentieth century as a transdisciplinary approach connecting the fields of electrical and computer engineering, mechanical engineering, dynamical systems theory, logic and discrete mathematical modeling, neuroscience, and other disciplines, cybernetics has greatly expanded in scope, addressing salient issues across the disciplinary spectrum, including the social sciences and the humanities. …”
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Differentiability of the Largest Lyapunov Exponent for Non-Planar Open Billiards by Amal Al Dowais

“…Our findings contribute to the field of dynamical systems theory and have significant implications for the stability of open billiard systems, which are used to model physical phenomena. …”
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One parameter is always enough by Steven T. Piantadosi

“…To achieve this, we apply results about the logistic map, an iterated map in dynamical systems theory that can be solved exactly. The existence of an equation fθ with this property highlights that “parameter counting” fails as a measure of model complexity when the class of models under consideration is only slightly broad.…”
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Learning from the past: reservoir computing using delayed variables by Ulrich Parlitz, Ulrich Parlitz

“…Reservoir computing is a machine learning method that is closely linked to dynamical systems theory. This connection is highlighted in a brief introduction to the general concept of reservoir computing. …”
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