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A monotoneiterative method for finding periodic solutions of an impulsive competition system on tumornormal cell interaction
1.  College of Mathematics and Information Science, Shanxi Normal University, Xi'an 710062, China 
2.  Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, China 
3.  Research Center for Applied Mathematics, Xi'an Jiaotong University, Xi'an, 710049, China 
[1] 
Yuanshi Wang, Hong Wu. Transition of interaction outcomes in a facilitationcompetition system of two species. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 14631475. doi: 10.3934/mbe.2017076 
[2] 
Martina Conte, Maria Groppi, Giampiero Spiga. Qualitative analysis of kineticbased models for tumorimmune system interaction. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 23932414. doi: 10.3934/dcdsb.2018060 
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M. Guedda, R. Kersner, M. Klincsik, E. Logak. Exact wavefronts and periodic patterns in a competition system with nonlinear diffusion. Discrete & Continuous Dynamical Systems  B, 2014, 19 (6) : 15891600. doi: 10.3934/dcdsb.2014.19.1589 
[4] 
Janet Dyson, Rosanna VillellaBressan, G. F. Webb. The evolution of a tumor cord cell population. Communications on Pure & Applied Analysis, 2004, 3 (3) : 331352. doi: 10.3934/cpaa.2004.3.331 
[5] 
Hongxia Yin. An iterative method for general variational inequalities. Journal of Industrial & Management Optimization, 2005, 1 (2) : 201209. doi: 10.3934/jimo.2005.1.201 
[6] 
Xiongxiong Bao, WanTong Li, ZhiCheng Wang. Uniqueness and Stability of TimePeriodic Pyramidal Fronts for a Periodic CompetitionDiffusion System. Communications on Pure & Applied Analysis, 2020, 19 (1) : 253277. doi: 10.3934/cpaa.2020014 
[7] 
João Fialho, Feliz Minhós. High order periodic impulsive problems. Conference Publications, 2015, 2015 (special) : 446454. doi: 10.3934/proc.2015.0446 
[8] 
Jingli Ren, Zhibo Cheng, Stefan Siegmund. Positive periodic solution for Brillouin electron beam focusing system. Discrete & Continuous Dynamical Systems  B, 2011, 16 (1) : 385392. doi: 10.3934/dcdsb.2011.16.385 
[9] 
Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 11411156. doi: 10.3934/mbe.2015.12.1141 
[10] 
Guanghui Hu, Andreas Kirsch, Tao Yin. Factorization method in inverse interaction problems with biperiodic interfaces between acoustic and elastic waves. Inverse Problems & Imaging, 2016, 10 (1) : 103129. doi: 10.3934/ipi.2016.10.103 
[11] 
Dan Liu, Shigui Ruan, Deming Zhu. Stable periodic oscillations in a twostage cancer model of tumor and immune system interactions. Mathematical Biosciences & Engineering, 2012, 9 (2) : 347368. doi: 10.3934/mbe.2012.9.347 
[12] 
Aleksa Srdanov, Radiša Stefanović, Aleksandra Janković, Dragan Milovanović. "Reducing the number of dimensions of the possible solution space" as a method for finding the exact solution of a system with a large number of unknowns. Mathematical Foundations of Computing, 2019, 2 (2) : 8393. doi: 10.3934/mfc.2019007 
[13] 
LiJun Du, WanTong Li, JiaBing Wang. Invasion entire solutions in a time periodic LotkaVolterra competition system with diffusion. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 11871213. doi: 10.3934/mbe.2017061 
[14] 
Morten Brøns. An iterative method for the canard explosion in general planar systems. Conference Publications, 2013, 2013 (special) : 7783. doi: 10.3934/proc.2013.2013.77 
[15] 
Lingling Lv, Zhe Zhang, Lei Zhang, Weishu Wang. An iterative algorithm for periodic sylvester matrix equations. Journal of Industrial & Management Optimization, 2018, 14 (1) : 413425. doi: 10.3934/jimo.2017053 
[16] 
Daniel Vasiliu, Jianjun Paul Tian. Periodic solutions of a model for tumor virotherapy. Discrete & Continuous Dynamical Systems  S, 2011, 4 (6) : 15871597. doi: 10.3934/dcdss.2011.4.1587 
[17] 
Jian Fang, Jianhong Wu. Monotone traveling waves for delayed LotkaVolterra competition systems. Discrete & Continuous Dynamical Systems  A, 2012, 32 (9) : 30433058. doi: 10.3934/dcds.2012.32.3043 
[18] 
YuHsien Chang, GuoChin Jau. The behavior of the solution for a mathematical model for analysis of the cell cycle. Communications on Pure & Applied Analysis, 2006, 5 (4) : 779792. doi: 10.3934/cpaa.2006.5.779 
[19] 
Sören Bartels, Marijo Milicevic. Iterative finite element solution of a constrained total variation regularized model problem. Discrete & Continuous Dynamical Systems  S, 2017, 10 (6) : 12071232. doi: 10.3934/dcdss.2017066 
[20] 
Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. ElDessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 37713782. doi: 10.3934/dcdsb.2017189 
2018 Impact Factor: 1.008
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