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On the approximation of the limit cycles function
"... We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function l. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero o ..."
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We consider planar vector fields depending on a real parameter. It is assumed that this vector field has a family of limit cycles which can be described by means of the limit cycles function l. We prove a relationship between the multiplicity of a limit cycle of this family and the order of a zero
On the number of limit cycles of the
, 1997
"... In this paper, we study a Liénard system of the form ˙x = y−F(x) , ˙y = −x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit ..."
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In this paper, we study a Liénard system of the form ˙x = y−F(x) , ˙y = −x, where F(x) is an odd polynomial. We introduce a method that gives a sequence of algebraic approximations to the equation of each limit cycle of the system. This sequence seems to converge to the exact equation of each limit
Credit Cycles
 Journal of Political Economy
, 1997
"... We construct a model of a dynamic economy in which lenders cannot force borrowers to repay their debts unless the debts are secured. In such an economy, durable assets play a dual role: not only are they factors of production, but they also serve as collateral for loans. The dynamic interaction betw ..."
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Cited by 1628 (36 self)
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between credit limits and asset prices turns out to be a powerful transmission mechanism by which the effects of shocks persist, amplify, and spill over to other sectors. We show that small, temporary shocks to technology or income distribution can generate large, persistent fluctuations in output
Analysis and Control of Limit Cycle
"... Abstract. The chapter addresses bifurcations of limit cycles for a general class of nonlinear control systems depending on parameters. A set of simple approximate analytical conditions characterizing all generic limit cycle bifurcations is determined via a first order harmonic balance analysis in a ..."
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Abstract. The chapter addresses bifurcations of limit cycles for a general class of nonlinear control systems depending on parameters. A set of simple approximate analytical conditions characterizing all generic limit cycle bifurcations is determined via a first order harmonic balance analysis
BIFURCATIONS AND LIMIT CYCLES IN THE
"... KEY WORDS limit cycles; bifurcations; noise; chaos; stochastic resonance; neural coding; variability ABSTRACT Based on insight obtained from a newly developed cochlea model, we argue that noisedriven limit cycles are the basic ingredient in the mammalian cochlea hearing process. For insect auditio ..."
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KEY WORDS limit cycles; bifurcations; noise; chaos; stochastic resonance; neural coding; variability ABSTRACT Based on insight obtained from a newly developed cochlea model, we argue that noisedriven limit cycles are the basic ingredient in the mammalian cochlea hearing process. For insect
1.1 Limit Cycles
"... In thefirstexperiment of this laboratory, weexamine a sourcecode exampleof acascaded biquad IIR filter implemented in fixedpoint arithmetic. The second task deals with zeroinput limit cycles in fixedpoint IIR filters. ..."
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In thefirstexperiment of this laboratory, weexamine a sourcecode exampleof acascaded biquad IIR filter implemented in fixedpoint arithmetic. The second task deals with zeroinput limit cycles in fixedpoint IIR filters.
Limit Cycles in Four Dimensions
, 2012
"... We present an example of a limit cycle, i.e., a recurrent flowline of the betafunction vector field, in a unitary fourdimensional gauge theory. We thus prove that beta functions of fourdimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation theory ..."
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We present an example of a limit cycle, i.e., a recurrent flowline of the betafunction vector field, in a unitary fourdimensional gauge theory. We thus prove that beta functions of fourdimensional gauge theories do not produce gradient flows. The limit cycle is established in perturbation
Excitatory and inhibitory interactions in localized populations of model
 Biophysics
, 1972
"... ABSMAcr Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The res ..."
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Cited by 491 (11 self)
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. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency ofthe limit cycle oscillationis found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics
Limit cycles and Lie symmetries ∗
"... Given a planar vector field U which generates the Lie symmetry of some other vector field X, we prove a new criterion to control the stability of the periodic orbits of U. The problem is linked to a classical problem proposed by A.T. Winfree in the seventies about the existence of isochrons of limit ..."
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of limit cycles (the question suggested by the study of biological clocks), already answered by Guckenheimer using a different terminology. We apply our criterion to give upper bounds of the number of limit cycles for some families of vector fields as well as to provide a class of vector fields with a
Results 1  10
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1,507,970