The Experts below are selected from a list of 105129 Experts worldwide ranked by ideXlab platform
Maoan Han - One of the best experts on this subject based on the ideXlab platform.
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small amplitude limit cycles of polynomial lienard systems
Science China-mathematics, 2013Co-Authors: Maoan Han, Yun TianAbstract:In this paper, we study the Number of limit cycles appeared in Hopf bifurcations of a Lienard system with multiple parameters. As an application to some polynomial Lienard systems of the form .x = y, .y = −gm(x) − fn(x)y, we obtain a new lower bound of Maximal Number of limit cycles which appear in Hopf bifurcation for arbitrary degrees m and n.
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bifurcation of limit cycles by perturbing a piecewise linear hamiltonian system
Abstract and Applied Analysis, 2013Co-Authors: Yanqin Xiong, Maoan HanAbstract:This paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. By using the first-order Melnikov function of the piecewise near-Hamiltonian system, we investigate the Maximal Number of limit cycles that bifurcate from a global center up to first order of .
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limit cycle bifurcations of some lienard systems with a cuspidal loop and a homoclinic loop
Chaos Solitons & Fractals, 2011Co-Authors: Junmin Yang, Maoan HanAbstract:Abstract In this paper, we study the Number of limit cycles of some polynomial Lienard systems with a cuspidal loop and a homoclinic loop, and obtain some new results on the lower bound of the Maximal Number of limit cycles for these systems.
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small amplitude limit cycles of some lienard type systems
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Jiao Jiang, Maoan HanAbstract:Abstract As we know, the Lienard system and its generalized forms are classical and important models of nonlinear oscillators, and have been widely studied by mathematicians and scientists. The main problem considered by most people is the Number of limit cycles. In this paper, we investigate two kinds of Lienard systems and obtain the Maximal Number (i.e. the least upper bound) of limit cycles appearing in Hopf bifurcations by applying some known bifurcation theorems with technical analysis.
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on hopf cyclicity of planar systems
Journal of Mathematical Analysis and Applications, 2000Co-Authors: Maoan HanAbstract:We investigate the Maximal Number of limit cycles which appear under perturbations in Hopf bifurcations by using the first-order Melnikov function with multiple parameters.
Jean Bertoin - One of the best experts on this subject based on the ideXlab platform.
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on largest offspring in a critical branching process with finite variance
Journal of Applied Probability, 2013Co-Authors: Jean BertoinAbstract:Continuing the work in Bertoin (2011) we study the distribution of the Maximal Number Xk* of offspring amongst all individuals in a critical Galton-Watson process started with k ancestors, treating the case when the reproduction law has a regularly varying tail ... with index -a for a > 2 (and, hence, finite variance). We show that Xk* suitably normalized converges in distribution to a Frechet law with shape parameter a/2; this contrasts sharply with the case 1 < a < 2 when the variance is infinite. More generally, we obtain a weak limit theorem for the offspring sequence ranked in decreasing order, in terms of atoms of a certain doubly stochastic Poisson measure.
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on the Maximal offspring in a critical branching process with infinite variance
Journal of Applied Probability, 2011Co-Authors: Jean BertoinAbstract:We investigate the Maximal Number $M_k$ of offsprings amongst all individuals in a critical Galton-Watson process started with $k$ ancestors. We show that when the reproduction law has a regularly varying tail with index $-\alpha$ for $1<\alpha<2$, then $k^{-1}M_k$ converges in distribution to a Frechet law with shape parameter $1$ and scale parameter depending only on $\alpha$.
Yanqin Xiong - One of the best experts on this subject based on the ideXlab platform.
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bifurcation of limit cycles by perturbing a piecewise linear hamiltonian system
Abstract and Applied Analysis, 2013Co-Authors: Yanqin Xiong, Maoan HanAbstract:This paper concerns limit cycle bifurcations by perturbing a piecewise linear Hamiltonian system. We first obtain all phase portraits of the unperturbed system having at least one family of periodic orbits. By using the first-order Melnikov function of the piecewise near-Hamiltonian system, we investigate the Maximal Number of limit cycles that bifurcate from a global center up to first order of .
Daniel Temesvari - One of the best experts on this subject based on the ideXlab platform.
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moments of the Maximal Number of empty simplices of a random point set
Discrete and Computational Geometry, 2018Co-Authors: Daniel TemesvariAbstract:For a finite set X of n points from $$ \mathbb {R}^M$$ , the degree of an M-element subset $$\{x_1,\dots ,x_M\}$$ of X is defined as the Number of M-simplices that can be constructed from this M-element subset using an additional point $$z \in X$$ , such that no further point of X lies in the interior of this M-simplex. Furthermore, the degree of X, denoted by $$\deg (X)$$ , is the Maximal degree of any of its M-element subsets. The purpose of this paper is to show that the moments of the degree of X satisfy $$\mathbb {E}\,[ \deg (X)^k ] \ge c n^k/\log n$$ , for some constant $$c>0$$ , if the elements of the set X are chosen uniformly and independently from a convex body $$W \subset \mathbb {R}^M$$ . Additionally, it will be shown that $$\deg (X)$$ converges in probability to infinity as the Number of points of the set X goes to infinity.
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moments of the Maximal Number of empty simplices of a random point set
arXiv: Probability, 2016Co-Authors: Daniel TemesvariAbstract:For a finite set $X$ of $n$ points from $\mathbb{R}^M$, the degree of an $M$-element subset $\{x_1,\dots,x_M\}$ of $X$ is defined as the Number of $M$-simplices that can be constructed from this $M$-element subset using an additional point $z\in X$, such that no further point of $X$ lies in the interior of this $M$-simplex. Furthermore, the degree of $X$, denoted by $\textrm{deg} (X)$, is the Maximal degree of any of its $M$-element subsets. The purpose of this paper is to show that the moments of the degree of $X$ satisfy $\mathbb{E}\left[\textrm{deg} (X)^k\right] \geq c n^k / \log n$, for some constant $c>0$, if the elements of the set $X$ are chosen uniformly and independently from a convex body $W \subset \mathbb{R}^M$. Additionally, it will be shown that these moments converge in probability to infinity as the Number of points of the set $X$ goes to infinity.
M Lakshmanan - One of the best experts on this subject based on the ideXlab platform.
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a systematic method of finding linearizing transformations for nonlinear ordinary differential equations i scalar case
Journal of Nonlinear Mathematical Physics, 2012Co-Authors: V K Chandrasekar, M Senthilvelan, M LakshmananAbstract:In this paper we formulate a stand alone method to derive Maximal Number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer Number of integrals of motion. The proposed algorithm is simple, straightforward and efficient and helps to unearth several new types of linearizing transformations besides the known ones in the literature. To make our studies systematic we divide our analysis into two parts. In the first part we confine our investigations to the scalar ODEs and in the second part we focus our attention on a system of two coupled second-order ODEs. In the case of scalar ODEs, we consider second and third-order nonlinear ODEs in detail and discuss the method of deriving Maximal Number of linearizing transformations irrespective of whether it is local or nonlocal type and illustrate the underlying theory with suitable examples. As a by-product of this investigation we unearth a new type of linearizing transfo...
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a systematic method of finding linearizing transformations for nonlinear ordinary differential equations i scalar case
arXiv: Exactly Solvable and Integrable Systems, 2010Co-Authors: V K Chandrasekar, M Senthilvelan, M LakshmananAbstract:In this set of papers we formulate a stand alone method to derive Maximal Number of linearizing transformations for nonlinear ordinary differential equations (ODEs) of any order including coupled ones from a knowledge of fewer Number of integrals of motion. The proposed algorithm is simple, straightforward and efficient and helps to unearth several new types of linearizing transformations besides the known ones in the literature. To make our studies systematic we divide our analysis into two parts. In the first part we confine our investigations to the scalar ODEs and in the second part we focuss our attention on a system of two coupled second order ODEs. In the case of scalar ODEs, we consider second and third order nonlinear ODEs in detail and discuss the method of deriving Maximal Number of linearizing transformations irrespective of whether it is local or nonlocal type and illustrate the underlying theory with suitable examples. As a by-product of this investigation we unearth a new type of linearizing transformation in third order nonlinear ODEs. Finally the study is extended to the case of general scalar ODEs. We then move on to the study of two coupled second order nonlinear ODEs in the next part and show that the algorithm brings out a wide variety of linearization transformations. The extraction of Maximal Number of linearizing transformations in every case is illustrated with suitable examples.
