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Averaging approach to cyclicity of Hopf bifurcation in planar linear-quadratic polynomial discontinuous differential systems

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 10, Pages : 3953 - 3965, 2017

Xingwu Chen - (email), Jaume Llibre - (email), Weinian Zhang - (email)

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Limit cycles for regularized discontinuous dynamical systems with a hyperplane of discontinuity

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 8, Pages : 3091 - 3112, 2017

Luca Dieci - (email), Cinzia Elia - (email), Dingheng Pi - (email)

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Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 9, Pages : 3259 - 3272, 2017

Jackson Itikawa - (email), Jaume Llibre - (email), Ana Cristina Mereu - (email), Regilene Oliveira - (email)

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Limit cycle bifurcations for piecewise smooth integrable differential systems

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 6, Pages : 2417 - 2425, 2017

Jihua Yang - (email), Liqin Zhao - (email)

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Global phase portrait of a degenerate Bogdanov-Takens system with symmetry

Discrete and Continuous Dynamical Systems - Series B  Volume 22, Issue 4, Pages : 1273 - 1293, 2017

Hebai Chen - (email), Xingwu Chen - (email), Jianhua Xie - (email)

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Cyclicity of a class of polynomial nilpotent center singularities

Discrete and Continuous Dynamical Systems  Volume 36, Issue 5, Pages : 2497 - 2520, 2015

Isaac A. García - (email), Douglas S. Shafer - (email)

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Cyclicity of some Liénard Systems

Communications on Pure and Applied Analysis  Volume 14, Issue 6, Pages : 2127 - 2150, 2015

Na Li - (email), Maoan Han - (email), Valery G. Romanovski - (email)

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Stability of singular limit cycles for Abel equations

Discrete and Continuous Dynamical Systems  Volume 35, Issue 5, Pages : 1873 - 1890, 2014

José Luis Bravo - (email), Manuel Fernández - (email), Armengol Gasull - (email)

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On the limit cycles bifurcating from an ellipse of a quadratic center

Discrete and Continuous Dynamical Systems  Volume 35, Issue 3, Pages : 1091 - 1102, 2014

Jaume Llibre - (email), Dana Schlomiuk - (email)

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Global dynamics of a piece-wise epidemic model with switching vaccination strategy

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 9, Pages : 2915 - 2940, 2014

Aili Wang - (email), Yanni Xiao - (email), Robert A. Cheke - (email)

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Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model

Discrete and Continuous Dynamical Systems - Series B  Volume 19, Issue 3, Pages : 747 - 760, 2014

Michael Y. Li - (email), Xihui Lin - (email), Hao Wang - (email)

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Dynamics of a ratio-dependent predator-prey system with a strong Allee effect

Discrete and Continuous Dynamical Systems - Series B  Volume 18, Issue 9, Pages : 2283 - 2313, 2013

Yujing Gao - (email), Bingtuan Li - (email)

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Piecewise linear perturbations of a linear center

Discrete and Continuous Dynamical Systems  Volume 33, Issue 9, Pages : 3915 - 3936, 2013

Claudio Buzzi - (email), Claudio Pessoa - (email), Joan Torregrosa - (email)

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Uniqueness of limit cycles and multiple attractors in a Gause-type predator-prey model with nonmonotonic functional response and Allee effect on prey

Mathematical Biosciences and Engineering  Volume 10, Issue 2, Pages : 345 - 367, 2013

Eduardo González-Olivares - (email), Betsabé González-Yañez - (email), Jaime Mena-Lorca - (email), José D. Flores - (email)

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15

On the number of limit cycles in general planar piecewise linear systems

Discrete and Continuous Dynamical Systems  Volume 32, Issue 6, Pages : 2147 - 2164, 2012

Song-Mei Huan - (email), Xiao-Song Yang - (email)

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16

Sharp upperbounds for the number of large amplitude limit cycles in polynomial Lienard systems

Discrete and Continuous Dynamical Systems  Volume 32, Issue 5, Pages : 1465 - 1479, 2012

Freddy Dumortier - (email)

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17

The center--focus problem and small amplitude limit cycles in rigid systems

Discrete and Continuous Dynamical Systems  Volume 32, Issue 5, Pages : 1627 - 1637, 2012

Fabio Scalco Dias - (email), Luis Fernando Mello - (email)

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The cyclicity of the period annulus of a class of quadratic reversible system

Communications on Pure and Applied Analysis  Volume 11, Issue 3, Pages : 1269 - 1283, 2011

Yi Shao - (email), Yulin Zhao - (email)

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Box dimension and bifurcations of one-dimensional discrete dynamical systems

Discrete and Continuous Dynamical Systems  Volume 32, Issue 4, Pages : 1287 - 1307, 2011

Lana Horvat Dmitrović - (email)

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The geometry of limit cycle bifurcations in polynomial dynamical systems

DCDS Supplements  Volume 2011, Issue Special, Pages : 447 - 456, 2011

Valery A. Gaiko - (email)

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On the birth of minimal sets for perturbed reversible vector fields

Discrete and Continuous Dynamical Systems  Volume 31, Issue 3, Pages : 763 - 777, 2011

Jaume Llibre - (email), Ricardo Miranda Martins - (email), Marco Antonio Teixeira - (email)

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Estimates on the number of limit cycles of a generalized Abel equation

Discrete and Continuous Dynamical Systems  Volume 31, Issue 1, Pages : 25 - 34, 2011

Naeem M. H. Alkoumi - (email), Pedro J. Torres - (email)

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Novel dynamics of a simple Daphnia-microparasite model with dose-dependent infection

Discrete and Continuous Dynamical Systems - Series S  Volume 4, Issue 6, Pages : 1599 - 1610, 2010

Kaifa Wang - (email), Yang Kuang - (email)

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Phase portraits, Hopf bifurcations and limit cycles of Leslie-Gower predator-prey systems with harvesting rates

Discrete and Continuous Dynamical Systems - Series B  Volume 14, Issue 1, Pages : 289 - 306, 2010

C. R. Zhu - (email), K. Q. Lan - (email)

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Cyclicity of unbounded semi-hyperbolic 2-saddle cycles in polynomial Lienard systems

Discrete and Continuous Dynamical Systems  Volume 27, Issue 3, Pages : 963 - 980, 2010

Magdalena Caubergh - (email), Freddy Dumortier - (email), Stijn Luca - (email)

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26

Upper bounds for the number of limit cycles of some planar polynomial differential systems

Discrete and Continuous Dynamical Systems  Volume 27, Issue 1, Pages : 217 - 229, 2010

Armengol Gasull - (email), Hector Giacomini - (email)

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Quadratic perturbations of a class of quadratic reversible systems with one center

Discrete and Continuous Dynamical Systems  Volume 27, Issue 1, Pages : 325 - 335, 2010

Haihua Liang - (email), Yulin Zhao - (email)

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Detecting alien limit cycles near a Hamiltonian 2-saddle cycle

Discrete and Continuous Dynamical Systems  Volume 25, Issue 4, Pages : 1081 - 1108, 2009

Stijn Luca - (email), Freddy Dumortier - (email), Magdalena Caubergh - (email), Robert Roussarie - (email)

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29

$3$ - dimensional Hopf bifurcation via averaging theory of second order

Discrete and Continuous Dynamical Systems  Volume 25, Issue 4, Pages : 1287 - 1295, 2009

Jaume Llibre - (email), Amar Makhlouf - (email), Sabrina Badi - (email)

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30

Relaxation oscillation profile of limit cycle in predator-prey system

Discrete and Continuous Dynamical Systems - Series B  Volume 11, Issue 4, Pages : 893 - 911, 2009

Sze-Bi Hsu - (email), Junping Shi - (email)

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31

Quadratic perturbations of a class of quadratic reversible systems with two centers

Discrete and Continuous Dynamical Systems  Volume 24, Issue 3, Pages : 699 - 729, 2009

B. Coll - (email), Chengzhi Li - (email), Rafel Prohens - (email)

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32

On the number of limit cycles of a cubic Near-Hamiltonian system

Discrete and Continuous Dynamical Systems  Volume 24, Issue 3, Pages : 827 - 840, 2009

Junmin Yang - (email), Maoan Han - (email)

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33

The number of limit cycles for generalized Abel equations with periodic coefficients of definite sign

Communications on Pure and Applied Analysis  Volume 8, Issue 5, Pages : 1493 - 1501, 2009

Amelia Álvarez - (email), José-Luis Bravo - (email), Manuel Fernández - (email)

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34

Seventeen limit cycles bifurcations of a fifth system

DCDS Supplements  Volume 2007, Issue Special, Pages : 1070 - 1081, 2007

Yunming Zhou - (email), Desheng Shang - (email), Tonghua Zhang - (email)

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35

Complex dynamics of a simple epidemic model with a nonlinear incidence

Discrete and Continuous Dynamical Systems - Series B  Volume 8, Issue 1, Pages : 161 - 173, 2007

Jianquan Li - (email), Yicang Zhou - (email), Jianhong Wu - (email), Zhien Ma - (email)

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36

Alien limit cycles in rigid unfoldings of a Hamiltonian 2-saddle cycle

Communications on Pure and Applied Analysis  Volume 6, Issue 1, Pages : 1 - 21, 2006

Magdalena Caubergh - (email), Freddy Dumortier - (email), Robert Roussarie - (email)

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37

The cyclicity of period annuli of some classes of reversible quadratic systems

Discrete and Continuous Dynamical Systems  Volume 16, Issue 1, Pages : 157 - 177, 2006

G. Chen - (email), C. Li - (email), C. Liu - (email), Jaume Llibre - (email)

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38

Some bifurcation methods of finding limit cycles

Mathematical Biosciences and Engineering  Volume 3, Issue 1, Pages : 67 - 77, 2005

Maoan Han - (email), Tonghua Zhang - (email)

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39

A competition model of the chemostat with an external inhibitor

Mathematical Biosciences and Engineering  Volume 3, Issue 1, Pages : 111 - 123, 2005

Jianquan Li - (email), Zuren Feng - (email), Juan Zhang - (email), Jie Lou - (email)

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40

The Role Of Time Delays, Slow Processes And Chaos In Modulating The Cell-Cycle Clock

Mathematical Biosciences and Engineering  Volume 2, Issue 3, Pages : 625 - 642, 2005

E.V. Presnov - (email), Z. Agur - (email)

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41

Twelve limit cycles in a cubic order planar system with $Z_2$- symmetry

Communications on Pure and Applied Analysis  Volume 3, Issue 3, Pages : 515 - 526, 2004

P. Yu - (email), M. Han - (email)

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42

The impact of state feedback control on a predator-prey model with functional response

Discrete and Continuous Dynamical Systems - Series B  Volume 4, Issue 3, Pages : 607 - 614, 2004

Haiying Jing - (email), Zhaoyu Yang - (email)

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43

A numerical investigation of the dynamics of a system of two time-delay coupled relaxation oscillators

Communications on Pure and Applied Analysis  Volume 2, Issue 4, Pages : 567 - 577, 2003

Richard H. Rand - (email), Asok K. Sen - (email)

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