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Wyniki wyszukiwania dla: GENERALIZED DYNAMICAL SYSTEMS
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Connection matrix theory for discrete dynamical systems
PublikacjaIn [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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Geometric methods in dynamical systems modelling: electrical, mechanical and control systems
PublikacjaRozważono 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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Index filtrations and Morse decomposition for discrete dynamical systems
PublikacjaOn 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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Stability by linear approximation for time scale dynamical systems
PublikacjaWe 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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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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Recent development in rigorous computational methods in dynamical systems
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Non-regular, incomplete and singular dynamical systems: impasse points indynamical systems
PublikacjaRozważono nieregularne, niezupełne i osobliwe różniczkowe systemy dynamicznez zastosowaniem metod geometrii różniczkowej.
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Frequency response based identification of fractional order dynamical systems
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Periodic Solutions of Generalized Lagrangian Systems with Small Perturbations
PublikacjaIn 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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Generalized Savitzky–Golay filters for identification of nonstationary systems
PublikacjaThe problem of identification of nonstationary systems using noncausal estimation schemes is consid-ered and a new class of identification algorithms, combining the basis functions approach with localestimationtechnique,isdescribed.Unliketheclassicalbasisfunctionestimationschemes,theproposedlocal basis function estimators are not used to obtain interval approximations of the parametertrajectory, but provide a sequence of point...
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Generalized quazilinearization for systems of degenerate singular perturbation problem
PublikacjaPraca dotyczy ogólnej metody kwazilinearyzacji dla układów równań różniczkowych z parametrami.
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Designing optimal and safe control strategies for time-varying dynamical systems
PublikacjaPublikacja 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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Generalized adaptive notch smoothers for real-valued signals and systems
PublikacjaSystems with quasi-periodically varying coefficients can be tracked using the algorithms known as generalized adaptive notch filters (GANFs). GANF algorithms can be considered an extension, to the system case, of classical adaptive notch filters (ANFs). We show that estimation accuracy of the existing algorithms, as well as their robustness to the choice of design parameters, can be considerably improved by means of compensating...
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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
PublikacjaArtykuł 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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Generalized adaptive notch filters with frequency debiasing for tracking of polynomial phase systems
PublikacjaGeneralized adaptive notch filters are used for identification/tracking of quasi-periodically varying dynamic systems and can be considered an extension, to the system case, of classical adaptive notch filters. For general patterns of frequency variation the generalized adaptive notch filtering algorithms yield biased frequency estimates. We show that when system frequencies change slowly in a smooth way, the estimation bias can...
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Regularized Identification of Time-Varying FIR Systems Based on Generalized Cross-Validation
PublikacjaA new regularization method is proposed and applied to identification of time-varying finite impulse response systems. We show, that by a careful design of the regularization constraint, one can improve estimation results, especially in the presence of strong measurement noise. We also show that the the most appropriate regularization gain can be found by direct optimization of the generalized cross-validation criterion.
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Adaptive Dynamical Systems Modelling of Transformational Organizational Change with Focus on Organizational Culture and Organizational Learning
PublikacjaTransformative 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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Adaptive Dynamical Systems Modelling of Transformational Organizational Change: with Focus on Organizational Culture and Organizational Learning
PublikacjaTransformative 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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Generalized adaptive notch and comb filters for identification of quasi-periodically varying systems
PublikacjaW artykule wprowadzono pojęcie obiektów pseudookresowych o parametrach będących liczbami rzeczywistymi. Pokazanometody oparte na metodzie funkcji bazowych pozwalające na identyfikację takich obiektów. Przedstawiono związekpomiędzy zaprojektowanymi algorytmami a klasycznymi filtrami wycinającymi typu notch.
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Firing map for periodically and almost-periodically driven integrate-and-fire models: a dynamical systems approach
PublikacjaWe 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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Discrete identification of continuous non-linear and non-stationary dynamical systems that is insensitive to noise correlation and measurement outliers
PublikacjaThe 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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Generalized adaptive comb filters/smoothers and their application to the identification of quasi-periodically varying systems and signals
PublikacjaThe problem of both causal and noncausal identification of linear stochastic systems with quasiharmonically varying parameters is considered. The quasi-harmonic description allows one to model nonsinusoidal quasi-periodic parameter changes. The proposed identification algorithms are called generalized adaptive comb filters/smoothers because in the special signal case they reduce down to adaptive comb algorithms used to enhance...
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Computational Analysis of Transformational Organisational Change with Focus on Organisational Culture and Organisational Learning: An Adaptive Dynamical Systems Modeling Approach
PublikacjaTransformative 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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Generalized regression neural network and fitness dependent optimization: Application to energy harvesting of centralized TEG systems
PublikacjaThe thermoelectric generator (TEG) system has attracted extensive attention because of its applications in centralized solar heat utilization and recoverable heat energy. The operating efficiency of the TEG system is highly affected by operating conditions. In a series-parallel structure, due to diverse temperature differences, the TEG modules show non-linear performance. Due to the non-uniform temperature distribution (NUTD) condition,...
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Billiard in a rotating half-plane
PublikacjaThe main objective of this research is to study the properties of a billiard system in an unbounded domain with moving boundary. We consider a system consisting of an infinite rod (a straight line) and a ball (a massless point) on the plane. The rod rotates uniformly around one of its points and experiences elastic collisions with the ball. We define a mathematical model for the dynamics of such a system and write down asymptotic...
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Fixed point indices of iterations of C^1 maps in R^3
PublikacjaW 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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General form of fixed point indices of an iterated C^1 map andinfiniteness of minimal periods
PublikacjaDla 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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Shadowing is generic---a continuous map case
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Partial hyperbolicity and central shadowing
PublikacjaWe 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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Distortion in the group of circle homeomorphisms
PublikacjaLet 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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Minimization of the number of periodic points for smooth self-maps of closed simply-connected 4-manifolds
PublikacjaLet 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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On quasi-compact Markov nets
PublikacjaAnalizuje 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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Periodic Points for Sphere Maps Preserving MonopoleFoliations
PublikacjaLet 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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Periodic points of latitudinal maps of the $m$-dimensional sphere
PublikacjaLet 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
PublikacjaIn 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
PublikacjaIn 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
PublikacjaA 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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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
PublikacjaExperimental 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...
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Rich Bifurcation Structure in a Two-Patch Vaccination Model
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Subharmonic solutions for a class of Lagrangian systems
PublikacjaWe prove that second order Hamiltonian systems with a potential of class C1, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [P. H. Rabinowitz, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38]. Indeed, we weaken...
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Wild oscillations in a nonlinear neuron model with resets: (I) Bursting, spike-adding and chaos
PublikacjaIn a series of two papers, we investigate the mechanisms by which complex oscillations are generated in a class of nonlinear dynamical systems with resets modeling the voltage and adaptation of neurons. This first paper presents mathematical analysis showing that the system can support bursts of any period as a function of model parameters, and that these are organized in a period-incrementing structure. In continuous dynamical...
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Wild oscillations in a nonlinear neuron model with resets: (II) Mixed-mode oscillations
PublikacjaThis work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically display a form of mixed-mode oscillations (MMOs), which are trajectories featuring an alternation of small oscillations with spikes or bursts (multiple consecutive spikes). The mechanism by...
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Detecting coupling directions with transcript mutual information: A comparative study
PublikacjaCausal relationships are important to understand the dynamics of coupled processes and, moreover, to influence or control the effects by acting on the causes. Among the different approaches to determine cause-effect relationships and, in particular, coupling directions in interacting random or deterministic processes, we focus in this paper on information-theoretic measures. So, we study in the theoretical part the difference between...
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The Arnold conjecture in $ \mathbb C\mathbb P^n $ and the Conley index
Publikacjan this paper we give an alternative, purely Conley index based proof of the Arnold conjecture in CP^n asserting that a Hamiltonian diffeomorphism of CP^n endowed with the Fubini-Study metric has at least (n+1) fixed points.
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Generalized Dold sequences on partially-ordered sets
PublikacjaDold sequences constitute an important class of integer sequences that play an important role in combinatorics, number theory, topology and dynamical systems. We generalize the notion of Dold sequence for the case of partially ordered sets and describe their properties. In particular we give two alternative descriptions of generalized Dold sequences: by some class of elementary sequences as well as by different...