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Search results for: ALMOST PERIODIC FUNCTIONS
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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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Integrate-and-fire models with an almost periodic input function
PublicationWe investigate leaky integrate-and-fire models (LIF models for short) driven by Stepanov and μ-almost periodic functions. Special attention is paid to the properties of the firing map and its displacement, which give information about the spiking behavior of the considered system. We provide conditions under which such maps are well-defined and are uniformly continuous. We show that the LIF models with Stepanov almost periodic...
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On delay differential equations with almost periodic boundary conditions started from different points
PublicationDyskutowany jest problem istnienia ekstremalnych rozwiązań dla równań różniczkowych typu opóźnionego przy odpowiednich warunkach brzegowych. Sformułowano odpowiednie twierdzenia porównawcze. W pracy zawarte są również wyniki dotyczące takich równań przy większej ilości argumentów opóźnionych.
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Toward a universal Embedded-Atom Method: II. A set of transferable denisty and dimmer referenced embedding energy functions for all elements of the periodic table as tool for removing two gauge degrees of freedom in EAM potentials
PublicationZestaw kluczowych właściwości homodwuatomowych cząsteczek o Z ≤ 103 (równowagowa odległość między atomami re, energia dysocjacji DO, Liczba falowa drgań ωe) zostały zestawione na bazie dostępnych danych eksperymantalnych oraz obliczeń za pomocą teorii funkcjonałów gęstości elektronowej B3LYP/SBKJC.
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Approximative sequences and almost homoclinic solutions for a class of second order perturbed Hamiltonian systems
PublicationIn this work we will consider a class of second order perturbed Hamiltonian systems with a superquadratic growth condition on a time periodic potential and a small aperiodic forcing term. To get an almost homoclinic solution we approximate the original system by time periodic ones with larger and larger time periods. These approximative systems admit periodic solutions, and an almost homoclinic solution for the original system...
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On the Existence of Homoclinic Type Solutions of a Class of Inhomogenous Second Order Hamiltonian Systems
PublicationWe show the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systems, where a C1-smooth potential satisfies a relaxed superquadratic growth condition, its gradient is bounded in the time variable, and a forcing term is sufficiently small in the space of square integrable functions. The idea of our proof is to approximate the original system by time-periodic ones, with larger and larger...
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Homoclinic orbits for an almost periodically forced singular Newtonian system in R^3
Publication. This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in R^3 which are subjected to almost periodic forcing in time variable
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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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A note on an approximative scheme of finding almost homoclinic solutions for Newtonian systems
PublicationIn this work we will be concerned with the existence of an almost homoclinic solution for a perturbed Newtonian system in a finite dimensional space. It is assumed that a potential is C^1 smooth and its gradient is bounded with respect to a time variable. Moreover, a forcing term is continuous, bounded and squere integrable. We will show that the appproximative scheme due to J. Janczewska for a time periodic potential extends to...
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On description of periodic magnetosonic perturbations in a quasi-isentropic plasma with mechanical and thermal losses and electrical resistivity
PublicationMagnetosonic periodic perturbations in a uniform and infinite plasma model are considered. Damping due to compressional viscosity, electrical resistivity, and thermal conduction are taken into account, as well as some heating–cooling function, which may destroy the isentropicity of wave perturbations. The wave vector forms arbitrary angle h with the equilibrium straight magnetic field, and all perturbations are functions...