Limit cycles of a class of planar polynomial differential systems
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DOI: 10.1002/mma.7645
Abstract: In this paper, we study the maximum number of limit cycles that can bifurcate from a linear center, when perturbed inside a class of planar polynomial differential systems of arbitrary degree n. Using averaging theory… read more here.
Keywords: class; class planar; planar polynomial; polynomial differential ... See more keywords
N-Dimensional Zero-Hopf Bifurcation of Polynomial Differential Systems via Averaging Theory of Second Order
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DOI: 10.1007/s10883-020-09501-6
Abstract: Using the averaging theory of second order, we study the limit cycles which bifurcate from a zero-Hopf equilibrium point of polynomial vector fields with cubic nonlinearities in ℝ n $\mathbb {R}^{n}$ . We prove that… read more here.
Keywords: averaging theory; second order; limit cycles; theory second ... See more keywords
Limit cycles for a class of discontinuous piecewise generalized Kukles differential systems
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DOI: 10.1007/s11071-018-4319-6
Abstract: The present paper is devoted to study an estimative to the number of limit cycles which bifurcate from the periodic orbits of the linear center $$\dot{x}=y, \dot{y}=-x$$x˙=y,y˙=-x by the averaging method of first order when… read more here.
Keywords: class discontinuous; differential systems; limit cycles; kukles differential ... See more keywords
Integrability and limit cycles in cubic Kukles systems with a nilpotent singular point
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DOI: 10.1007/s11071-019-04805-0
Abstract: In this paper, integrability problem and bifurcation of limit cycles for cubic Kukles systems which are assumed to have a nilpotent origin are investigated. A complete classification is given on the integrability conditions and proven… read more here.
Keywords: cubic kukles; kukles systems; integrability; limit cycles ... See more keywords
Bifurcation of limit cycles in piecewise-smooth systems with intersecting discontinuity surfaces
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DOI: 10.1007/s11071-019-05400-z
Abstract: This paper deals with bifurcation of limit cycles for perturbed piecewise-smooth systems. Concentrating on the case in which the vector fields are defined in four domains and the discontinuity surfaces are codimension-2 manifolds in the… read more here.
Keywords: limit cycles; discontinuity surfaces; bifurcation limit; piecewise smooth ... See more keywords
Qualitative Analysis of Crossing Limit Cycles in a Class of Discontinuous Liénard Systems with Symmetry
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DOI: 10.1007/s12346-018-0278-z
Abstract: In this paper, we investigate some qualitative properties of crossing limit cycles for a discontinuous symmetric Liénard system with two zones separated by a straight line. In each zone, it is a smooth Liénard system.… read more here.
Keywords: crossing limit; qualitative analysis; limit; limit cycle ... See more keywords
Higher Order Melnikov Functions for Studying Limit Cycles of Some Perturbed Elliptic Hamiltonian Vector Fields
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DOI: 10.1007/s12346-018-0284-1
Abstract: In this paper, we study the number of limit cycles in the perturbed Hamiltonian system $$dH=\varepsilon F_1+\varepsilon ^2 F_2+\varepsilon ^3 F_3$$dH=εF1+ε2F2+ε3F3 with $$F_i$$Fi, the vector valued homogeneous polynomials of degree i and $$4-i$$4-i for $$i=1,2,3$$i=1,2,3,… read more here.
Keywords: limit cycles; limit; higher order; melnikov functions ... See more keywords
A Linear Estimate of the Number of Limit Cycles for A Piecewise Smooth Near-Hamiltonian System
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DOI: 10.1007/s12346-020-00398-x
Abstract: In this paper, we study Poincaré bifurcation of limit cycles from a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop round the origin. By using the Melnikov function method,… read more here.
Keywords: limit cycles; limit; cycles piecewise; number limit ... See more keywords
On the Number of Limit Cycles in General Planar Piecewise Linear Differential Systems with Two Zones Having Two Real Equilibria
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DOI: 10.1007/s12346-020-00441-x
Abstract: A general family of planar piecewise linear ODEs with two zones both having a real focus and separated by a straight line is considered. By analyzing the number of zero points of a new function… read more here.
Keywords: planar piecewise; limit cycles; number; piecewise linear ... See more keywords
Several Bifurcation Mechanisms for Limit Cycles in a Predator–Prey System
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DOI: 10.1007/s12346-021-00501-w
Abstract: The research presented in this paper compares the occurrence of limit cycles under different bifurcation mechanisms in a simple system of two-dimensional autonomous predator–prey ODEs. Surprisingly two unconventional approaches, for a singular system and for… read more here.
Keywords: system; limit cycles; bifurcation mechanisms; predator prey ... See more keywords
Maximum Number of Limit Cycles for Generalized Kukles Polynomial Differential Systems
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DOI: 10.1007/s12591-016-0300-3
Abstract: We study the maximum number of limit cycles of the polynomial differential systems of the form $$\begin{aligned} \dot{x}=-y+l(x), \,\dot{y}=x-f(x)-g(x)y-h(x)y^{2}-d_{0}y^{3}, \end{aligned}$$x˙=-y+l(x),y˙=x-f(x)-g(x)y-h(x)y2-d0y3,where $$l(x)=\varepsilon l^{1}(x)+\varepsilon ^{2}l^{2}(x),$$l(x)=εl1(x)+ε2l2(x),$$f(x)=\varepsilon f^{1}(x)+\varepsilon ^{2}f^{2}(x),$$f(x)=εf1(x)+ε2f2(x),$$g(x)=\varepsilon g^{1}(x)+\varepsilon ^{2}g^{2}(x),$$g(x)=εg1(x)+ε2g2(x),$$h(x)=\varepsilon h^{1}(x)+\varepsilon ^{2}h^{2}(x)$$h(x)=εh1(x)+ε2h2(x) and $$d_{0}=\varepsilon d_{0}^{1}+\varepsilon ^{2}d_{0}^{2}$$d0=εd01+ε2d02 where $$l^{k}(x),$$lk(x),$$f^{k}(x),$$fk(x),$$g^{k}(x)$$gk(x)… read more here.
Keywords: number; maximum number; number limit; limit cycles ... See more keywords