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Search results for: dynamical systems
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Connection matrix theory for discrete dynamical systems
PublicationIn [C] and [F1] the connection matrix theory for Morse decomposition is developedin the case of continuous dynamical systems. Our purpose is to study the case of discrete timedynamical systems.
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Connection matrix theory for discrete dynamical systems
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Index filtrations and Morse decomposition for discrete dynamical systems
PublicationOn a Morse decomposition of an isolated invariant set of a homeomorphism(discrete dynamical system) there are partial orderings defined by the homeomorphism.These are called admissible orderings of the...
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Recent development in rigorous computational methods in dynamical systems
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Index filtrations and Morse decompositions for discrete dynamical systems
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Stability by linear approximation for time scale dynamical systems
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Stability by linear approximation for time scale dynamical systems
PublicationWe study systems on time scales that are generalizations of classical differential or difference equations and appear in numerical methods. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of matrices we formulate conditions, sufficient for stability by linear approximation. For non-periodic time scales we use techniques of central upper Lyapunov exponents...
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Geometric methods in dynamical systems modelling: electrical, mechanical and control systems
PublicationRozważono zagadnienia modelowania systemów dynamicznych z zastosowaniem metod geometrii różniczkowej. Równania dynamiczne otrzymano w postaci inkluzji różniczkowych. Przestrzenie konstytucyjne przyjęto w postaci subwiązek włóknistych. Rozważono przestrzenie konstytucyjne układów elektrycznych, układów mechanicznych i układów sterowania. Podstawowe wyniki pracy dotyczą struktury przestrzeni rozwiązań rozważanych systemów.
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Frequency response based identification of fractional order dynamical systems
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Non-regular, incomplete and singular dynamical systems: impasse points indynamical systems
PublicationRozważono nieregularne, niezupełne i osobliwe różniczkowe systemy dynamicznez zastosowaniem metod geometrii różniczkowej.
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Designing optimal and safe control strategies for time-varying dynamical systems
PublicationPublikacja opisuje metodę projektowania optymalnej trajektorii punktu pracy w czasoprzestrzeni stanów przy wykorzystaniu algorytmów optymalizacji grafowej. Zakłada się deterministyczny charakter zmian dynamiki rozpatrywanego procesu. Przestrzeń robocza, będąca ograniczonym podzbiorem czasoprzestrzeni stanów, jest dzielona na zbiór segmentów, którym przypisywane są wielkości reprezentujące właściwości dynamiki własnej w obrębie...
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Fractional Variable-Order Derivative and Difference Operators and Their Applications to Dynamical Systems Modelling
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Toolgraph Design of Optimal and Feasible Control Strategies for Time-Varying Dynamical Systems
PublicationArtykuł prezentuje nową metodę projektowania optymalnych i realizowanych strategii sterowania dla wariantnych procesów dynamicznych. Centralnym ośrodkiem i narzędziem tej metody jest struktura grafu przepływowego reprezentująca istotne właściwości autonomicznej dynamiki danego procesu w przestrzeni czasowo-stanowej, składającej się z elementarnych segmentów. Strukturę tę nazywamy grafem narzędziowym przestrzeni czasowo-stanowej....
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Adaptive Dynamical Systems Modelling of Transformational Organizational Change: with Focus on Organizational Culture and Organizational Learning
PublicationTransformative Organizational Change becomes more and more significant both practically and academically, especially in the context of organizational culture and learning. However computational modeling and a formalization of organizational change and learning processes are still largely unexplored. This paper aims to provide an adaptive network model of transformative organizational change and translate a selection of organizational...
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Firing map for periodically and almost-periodically driven integrate-and-fire models: a dynamical systems approach
PublicationWe consider the Leaky Integrate-and-Fire and Perfect Integrator models of neuron’s dynamics with the input function being periodic and almost-periodic (in the sense of Stepanov). In particular we analyze properties and dynamics of the so-called firing map, which iterations give timings of consecutive spikes of a neuron. In case of a periodic input function we provide a detailed description of the sequence of interspike-intervals,...
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Adaptive Dynamical Systems Modelling of Transformational Organizational Change with Focus on Organizational Culture and Organizational Learning
PublicationTransformative Organizational Change becomes more and more significant both practically and academically, especially in the context of organizational culture and learning. However computational modeling and a formalization of organizational change and learning processes are still largely unexplored. This paper aims to provide an adaptive network model of transformative organizational change and translate a selection of organizational...
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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublicationThe paper uses specific parameter estimation methods to identify the coefficients of continuous-time models represented by linear and non-linear ordinary differential equations. The necessary approximation of such systems in discrete time in the form of utility models is achieved by the use of properly tuned `integrating filters' of the FIR type. The resulting discrete-time descriptions retain the original continuous parameterization...
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Computational Analysis of Transformational Organisational Change with Focus on Organisational Culture and Organisational Learning: An Adaptive Dynamical Systems Modeling Approach
PublicationTransformative Organisational Change becomes more and more significant both practically and academically, especially in the context of organisational culture and learning. However computational modeling and formalization of organisational change and learning processes are still largely unexplored. This chapter aims to provide an adaptive network model of transformative organisational change and translate a selection of organisational...
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Nonautonomous Dynamical Systems
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DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
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Differential Equations and Dynamical Systems
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Advances in Dynamical Systems and Applications
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Qualitative Theory of Dynamical Systems
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Journal of Dynamical Systems and Geometric Theories
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MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS
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DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
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International Journal of Dynamical Systems and Differential Equations
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SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
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ERGODIC THEORY AND DYNAMICAL SYSTEMS
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DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL
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Topology and Dynamical Systems in Action - Summer school 2023
e-Learning CoursesThe course is designed for participants in the Spinnaker summer school in mathematics.
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Journal of Advanced Research in Dynamical and Control Systems
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Discrete and Continuous Dynamical Systems-Series S
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JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
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Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations
PublicationIn this paper we study the generalized Lagrangian system with a small perturbation. We assume the main term in the system to have a maximum, but do not suppose any condition for perturbation term. Then we prove the existence of a periodic solution via Ekeland’s principle. Moreover, we prove a convergence theorem for periodic solutions of perturbed systems.
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Distortion in the group of circle homeomorphisms
PublicationLet G be the group PAff+(R/Z) of piecewise affine circle homeomorphisms or the group Diff∞(R/Z) of smooth circle diffeomorphisms. A constructive proof that all irrational rotations are distorted in G is given.
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Shadowing is generic---a continuous map case
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General form of fixed point indices of an iterated C^1 map andinfiniteness of minimal periods
PublicationDla zwartego podzbioru punktów periodycznych gładkiego odwzorowania podana zostaje formuła na indeksy iteracji. Wynik stanowi uogólnienie rezultatu Chowa, Malleta-Pareta i Yorke'a.
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Fixed point indices of iterations of C^1 maps in R^3
PublicationW przypadku gładkiego odwzorowania w R^3 dowiedziona została hipoteza Chowa, Malleta-Pareta i Yorka dotycząca postaci ciągów indeksow iteracji oraz podano kompletny opis możliwych ciągów indeksow.
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Partial hyperbolicity and central shadowing
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On quasi-compact Markov nets
PublicationAnalizuje się strukturę ergodyczną netów Markowa. W szczególności podano charakteryzację ściśle ergodycznych minimalnych (L-R) netów markowskich na zwartej przestrzeni fazowej. Uzyskano warunki równoważne quasi-zwartości (L-R) netów Markowa, rozszerzając tzw. ergodyczne twierdzenie Lotz'a.
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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublicationLet M be a smooth closed simply-connected 4-dimensional manifold, f be a smooth self-map of M with fast grow of Lefschetz numbers and r be a product of different primes. The authors calculate the invariant equal to the minimal number of r-periodic points in the smooth homotopy class of f.
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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublicationLet f be a smooth self-map of the m-dimensional sphere Sm. Under the assumption that f preserves latitudinal foliations with the fibres S1, we estimate from below the number of fixed points of the iterates of f. The paper generalizes the results obtained by Pugh and Shub and by Misiurewicz.
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Distribution of the displacement sequence of an orientation preserving circle homeomorphism
PublicationIn some applications not only the knowledge of the behaviour of trajectories of a map is important, but also their displacements. We describe in detail the distribution of elements of the displacement sequence along a trajectory of an orientation preserving circle homeomorphism ϕ with irrational rotation number ϱ(ϕ). The values of displacement are dense in a set which depends on the map γ (semi-)conjugating ϕ with the rotation...
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Firing map of an almost periodic input function
PublicationIn mathematical biology and the theory of electric networks the firing map of an integrate-and-fire system is a notion of importance. In order to prove useful properties of this map authors of previous papers assumed that the stimulus function f of the system ẋ = f(t,x) is continuous and usually periodic in the time variable. In this work we show that the required properties of the firing map for the simplified model ẋ = f(t) still...
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Invariant Measures for Uncountable Random Interval Homeomorphisms
PublicationA necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions...
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Partial hyperbolicity and central shadowing
PublicationWe study shadowing property for a partially hyperbolic diffeomor- phism f. It is proved that if f is dynamically coherent then any pseudotrajec- tory can be shadowed by a pseudotrajectory with “jumps” along the central foliation. The proof is based on the Tikhonov-Shauder fixed point theorem.
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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublicationLet S^2 be a two-dimensional sphere. We consider two types of its foliations with one singularity and maps f:S^2→S^2 preserving these foliations, more and less regular. We prove that in both cases f has at least |deg(f)| fixed points, where deg(f) is a topological degree of f. In particular, the lower growth rate of the number of fixed points of the iterations of f is at least log|deg(f)|. This confirms the Shub’s conjecture in...
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A Database Schema for the Analysis of Global Dynamics of Multiparameter Systems
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Type III Responses to Transient Inputs in Hybrid Nonlinear Neuron Models
PublicationExperimental characterization of neuronal dynamics involves recording both of spontaneous activity patterns and of responses to transient and sustained inputs. While much theoretical attention has been devoted to the spontaneous activity of neurons, less is known about the dynamic mechanisms shaping their responses to transient inputs, although these bear significant physiological relevance. Here, we study responses to transient...