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Dive into the research topics where Changjian Liu is active.

Publication


Featured researches published by Changjian Liu.


Nonlinearity | 2012

On the hyperelliptic limit cycles of Liénard systems

Changjian Liu; Guoting Chen; Jiazhong Yang

In this paper we study hyperelliptic limit cycles of the Lienard systems where, respectively, fm(x) and gn(x) are polynomials of degree m and n, gn(0) = 0. We prove that, if m ≥ 5 and m + 1 < n < 2m, then there always exist Lienard systems of the above form such that they have a hyperelliptic limit cycle. This gives a positive answer to the open problem posed in the paper by Yu and Zhang (2011 J. Math. Anal. Appl. 376 535–9). By combining all the results obtained up to now, we in fact give a complete classification of the hyperelliptic limit cycles of the Lienard systems: Lienard systems of the above form have hyperelliptic limit cycles only in the following cases: (i) m = 2, 3 and m + 3 ≤ n; (ii) 4 ≤ m and m + 2 ≤ n.


Transactions of the American Mathematical Society | 2013

The monotonicity of the ratio of two Abelian integrals

Changjian Liu; Dongmei Xiao

In this paper, we study the monotonicity of the ratio of two Abelian integrals


Nonlinearity | 2012

Limit cycles bifurcated from some reversible quadratic centres with a non-algebraic first integral

Changjian Liu

We study the cyclicity of period annuli of some reversible non-Hamiltonian quadratic systems under quadratic perturbations. In general, the first integral, which we study, is non-algebraic. Via estimating the number of zeros of the associated Abelian integral (first order Melnikov function), we show that the cyclicity is 2.


Journal of Differential Equations | 2009

A cubic system with thirteen limit cycles

Chengzhi Li; Changjian Liu; Jiazhong Yang


Journal of Mathematical Analysis and Applications | 2012

Integrability of Lotka-Volterra type systems of degree 4

Changjian Liu; Guoting Chen; Guanrong Chen


Journal of Differential Equations | 2012

The cyclicity of period annuli of a class of quadratic reversible systems with two centers

Changjian Liu


Journal of Differential Equations | 2010

On the number of critical periods for planar polynomial systems of arbitrary degree

Armengol Gasull; Changjian Liu; Jiazhong Yang


Journal of Mathematical Analysis and Applications | 2015

A linear estimate of the number of limit cycles for some planar piecewise smooth quadratic differential system

Shimin Li; Changjian Liu


Journal of Mathematical Analysis and Applications | 2013

The cyclicity of period annuli of a class of quintic Hamiltonian systems

Liqin Zhao; Minghui Qi; Changjian Liu


Comptes Rendus Mathematique | 2013

Lyapunov exponent of a stochastic SIRS model

Guoting Chen; Tiecheng Li; Changjian Liu

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Dongmei Xiao

Shanghai Jiao Tong University

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Jicai Huang

Central China Normal University

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Jihua Wang

Sun Yat-sen University

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Liqin Zhao

Beijing Normal University

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Minghui Qi

Beijing Normal University

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Shimin Li

Guangdong University of Business Studies

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