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Zeitschrift für angewandte Mathematik und Physik : Volume 67

Zeitschrift für angewandte Mathematik und Physik : Volume 67, Issue 5, October 2016

Zeitschrift für angewandte Mathematik und Physik : Volume 67, Issue 4, August 2016

New results on averaging theory and applications

Multiple liquid bridges with non-smooth interfaces

Exact solutions for logistic reaction–diffusion equations in biology

2D steady-state general solution and fundamental solution for fluid-saturated, orthotropic, poroelastic materials

An implicit three-dimensional model for describing the inelastic response of solids undergoing finite deformation

A novel mathematical model for growth of capillaries and nutrient supply with application to prediction of osteophyte onset

The exact asymptotic behavior of boundary blow-up solutions to infinity Laplacian equations

Global solutions to a chemotaxis model with consumption of chemoattractant

On the problem of a thin rigid inclusion embedded in a Maxwell material

An explicit solution for the dynamics of a taut string of finite length carrying a traveling mass: the subsonic case

Debonding of an elastic inhomogeneity of arbitrary shape in anti-plane shear

Numerical identification procedure between a micro-Cauchy model and a macro-second gradient model for planar pantographic structures

Bed of polydisperse viscous spherical drops under thermocapillary effects

Ground state sign-changing solutions for a class of Schrödinger–Poisson type problems in $${\mathbb{R}^{3}}$$ R 3

Pullback attractors of the two-dimensional non-autonomous simplified Ericksen–Leslie system for nematic liquid crystal flows

Global regular solutions for the 3D Kawahara equation posed on unbounded domains

Torsional vibration of single-walled carbon nanotubes using doublet mechanics

Global well-posedness for the 2D dispersive SQG equation and inviscid Boussinesq equations

Gigahertz nanomechanical oscillators based on ions inside cyclic peptide nanotubes: a continuum study

Global smooth flows for compressible Navier–Stokes–Maxwell equations

Incompressible limit of all-time solutions to 3-D full Navier–Stokes equations for perfect gas with well-prepared initial condition

Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

Evolutionary dynamics of phenotype-structured populations: from individual-level mechanisms to population-level consequences

The formulation of dynamical contact problems with friction in the case of systems of rigid bodies and general discrete mechanical systems—Painlevé and Kane paradoxes revisited

Long-term behavior of reaction–diffusion equations with nonlocal boundary conditions on rough domains

Zeitschrift für angewandte Mathematik und Physik : Volume 67, Issue 3, June 2016

Zeitschrift für angewandte Mathematik und Physik : Volume 67, Issue 2, April 2016

Zeitschrift für angewandte Mathematik und Physik : Volume 67, Issue 1, March 2016

Zeitschrift für angewandte Mathematik und Physik : Volume 66

Zeitschrift für angewandte Mathematik und Physik : Volume 65

Zeitschrift für angewandte Mathematik und Physik : Volume 64

Zeitschrift für angewandte Mathematik und Physik : Volume 63

Zeitschrift für angewandte Mathematik und Physik : Volume 62

Zeitschrift für angewandte Mathematik und Physik : Volume 61

Zeitschrift für angewandte Mathematik und Physik : Volume 60

Zeitschrift für angewandte Mathematik und Physik : Volume 59

Zeitschrift für angewandte Mathematik und Physik : Volume 58

Zeitschrift für angewandte Mathematik und Physik : Volume 57

Zeitschrift für angewandte Mathematik und Physik : Volume 56

Zeitschrift für angewandte Mathematik und Physik : Volume 55

Zeitschrift für angewandte Mathematik und Physik : Volume 54

Zeitschrift für angewandte Mathematik und Physik : Volume 53

Zeitschrift für angewandte Mathematik und Physik : Volume 52

Zeitschrift für angewandte Mathematik und Physik : Volume 51

Zeitschrift für angewandte Mathematik und Physik : Volume 50

Zeitschrift für angewandte Mathematik und Physik : Volume 49

Zeitschrift für angewandte Mathematik und Physik : Volume 48

New results on averaging theory and applications

Content Provider	Springer Nature Link
Author	Cândido, Murilo R. Llibre, Jaume
Copyright Year	2016
Abstract	The usual averaging theory reduces the computation of some periodic solutions of a system of ordinary differential equations, to find the simple zeros of an associated averaged function. When one of these zeros is not simple, i.e., the Jacobian of the averaged function in it is zero, the classical averaging theory does not provide information about the periodic solution associated to a non-simple zero. Here we provide sufficient conditions in order that the averaging theory can be applied also to non-simple zeros for studying their associated periodic solutions. Additionally, we do two applications of this new result for studying the zero–Hopf bifurcation in the Lorenz system and in the Fitzhugh–Nagumo system.
Ending Page	11
Page Count	11
Starting Page	1
File Format	PDF
ISSN	00442275
e-ISSN	14209039
Journal	Zeitschrift für angewandte Mathematik und Physik
Issue Number	4
Volume Number	67
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-08-05
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Polynomial differential system Averaging method Fitzhugh–Nagumo system Mathematical Methods in Physics Periodic solutions Lorenz system Periodic orbits of vector fields and flows Averaging theory Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Physics and Astronomy

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Attraction Basin of the Equilibrium Configuration in the FitzHugh-Nagumo Model

Improving the averaging theory for computing periodic solutions of the differential equations

Limit cycles for m-piecewise discontinuous polynomial Liénard differential equations

Cyclicity versus Center Problem

Stability of Traveling Pulses with Oscillatory Tails in the FitzHugh–Nagumo System

On the existence and stability of periodic orbits in non ideal problems: General results

Extended quasi-homogeneous polynomial system in $${\mathbb{R}^{3}}$$

Existence of Periodic Solutions of the FitzHugh--Nagumo Equations for an Explicit Range of the Small Parameter

Limit cycles for some families of smooth and non-smooth planar systems

New results on averaging theory and applications

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Attraction Basin of the Equilibrium Configuration in the FitzHugh-Nagumo Model

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