Results 1  10
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49
Nonlinear eects in twolayer largeamplitude
, 1999
"... Baroclinic largeamplitude geostrophic (LAG) models, which assume a leadingorder geostrophic balance but allow for largeamplitude isopycnal deflections, provide a suitable framework to model the largeamplitude motions exhibited in frontal regions. The qualitative dynamical characterization of LAG ..."
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Baroclinic largeamplitude geostrophic (LAG) models, which assume a leadingorder geostrophic balance but allow for largeamplitude isopycnal deflections, provide a suitable framework to model the largeamplitude motions exhibited in frontal regions. The qualitative dynamical characterization
TWELVE LIMIT CYCLES IN A CUBIC CASE OF THE 16th HILBERT PROBLEM
, 2005
"... In this paper, we prove the existence of twelve small (local) limit cycles in a planar system with thirddegree polynomial functions. The best result so far in literature for a cubic order planar system is eleven limit cycles. The system considered in this paper has a saddle point at the origin and ..."
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Cited by 23 (17 self)
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In this paper, we prove the existence of twelve small (local) limit cycles in a planar system with thirddegree polynomial functions. The best result so far in literature for a cubic order planar system is eleven limit cycles. The system considered in this paper has a saddle point at the origin
Limit Cycle Bifurcations of a Special Liénard Polynomial System
"... In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit cycles surrounding a unique singular point for an arbitrary po ..."
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polynomial system. Then, by means of the same bifurcationally geometric approach, we solve the limit cycle problem for a Liénard system with cubic restoring and polynomial damping functions.
Twelve limit cycles in a cubic order planar system with Z2 symmetry
 COMMUN. PURE APPL. ANAL
, 2004
"... In this paper, we report the existence of twelve small limit cycles in a planar system with 3rddegree polynomial functions. The system has Z2symmetry, with a saddle point, or a node, or a focus point at the origin, and two focus points which are symmetric about the origin. It is shown that such ..."
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Cited by 2 (1 self)
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In this paper, we report the existence of twelve small limit cycles in a planar system with 3rddegree polynomial functions. The system has Z2symmetry, with a saddle point, or a node, or a focus point at the origin, and two focus points which are symmetric about the origin. It is shown
An application of regular chain theory to the study of limit cycles
 INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
"... In this paper, the theory of regular chains and a triangular decomposition method relying on modular computations are presented in order to symbolically solve multivariate polynomial systems. Based on the focus values for dynamic systems obtained by using normal form theory, this method is applied ..."
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is applied to compute the limit cycles bifurcating from Hopf critical points. In particular, a quadratic planar polynomial system is used to demonstrate the solving process and to show how to obtain center conditions. The modular computations based on regular chains are applied to a cubic planar polynomial
Effects of Cubic Hardening Nonlinearities on the Flutter of a Three Degree of Freedom Airfoil
"... This paper derives nonlinear second order ordinary differential equations describing the motion of a two dimensional airfoil allowing for three spatial degrees of freedom in the airfoil’s angular rotation, vertical movement, and control surface rotation. The equations of motion are derived from the ..."
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, it is demonstrated that it is possible to aeroelastically tailor the airfoil such that flutter is avoided for a given flight regime. Above the flutter speed, limit cycle oscillations are predicted that grow in amplitude with the airspeed. The amplitude of the limit cycles are also dependent on the posi
Liénard’s System and Smale’s Problem
, 2006
"... In this paper, using geometric properties of the field rotation parameters, we present a solution of Smale’s Thirteenth Problem on the maximum number of limit cycles for Liénard’s polynomial system. We also generalize the obtained result and present a solution of Hilbert’s Sixteenth Problem on the m ..."
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on the maximum number of limit cycles surrounding a singular point for an arbitrary polynomial system. Besides, we consider a generalized Liénard’s cubic system with three finite singularities, for which the developed geometric approach can complete its global qualitative analysis: in particular, it easily
Estimation of response spectra and peak accelerations from western North American earthquakes, U.S. Geological Survey OpenFile Report 93509
, 1993
"... INTRODUCTION More than a decade ago we presented equations for predicting peak horizontal acceleration and response spectra in terms of moment magnitude, distance, and site conditions for shallow earthquakes in western North America Boore, 1981, 1982). We are currently developing a new set of equ ..."
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Cited by 42 (1 self)
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, and 1993 Landers earthquakes have provided data in the critical largemagnitude, closedistance range, however, limiting the variations in predicted motions permitted by the data. To see if our data set would support a smaller magnitude scaling at short distance, we took residuals at stations within 10 km
Twodimensional Fuchsian systems and the Chebyshev property
 J. Differential Equations
"... Abstract. Let (x(t), y(t)) ⊤ be a solution of a Fuchsian system of order two with three singular points. The vector space of functions of the form P(t)x(t) + Q(t)y(t), where P, Q are real polynomials, has a natural filtration of vector spaces, according to the asymptotic behaviour of the functions ..."
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Cited by 3 (1 self)
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such a nonoscillation property. It is remarkable that most of these systems are of the type studied in the present paper. We apply our results in estimating the number of limit cycles that appear after small polynomial perturbations of several quadratic or cubic Hamiltonian systems in the plane. 2000 MSC
A Numerical Study of the Lorenz and LorenzStenflo Systems
"... ges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen ..."
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ges till offentlig granskning för avläggande av teknologie doktorsexamen fredagen
Results 1  10
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49