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Stability, delay, and chaotic behavior in a LotkaVolterra predatorprey system
A nonlinear $L^2$stability analysis for twospecies population dynamics with dispersal
1.  University of Naples Federico II, Department of Mathematics and Applications ''R. Caccioppoli", Complesso Universitario Monte S. Angelo. Via Cinzia, 80126 Napoli, Italy 
[1] 
Bo Duan, Zhengce Zhang. A twospecies weak competition system of reactiondiffusionadvection with double free boundaries. Discrete & Continuous Dynamical Systems  B, 2019, 24 (2) : 801829. doi: 10.3934/dcdsb.2018208 
[2] 
Xinfu Chen, KingYeung Lam, Yuan Lou. Corrigendum: Dynamics of a reactiondiffusionadvection model for two competing species. Discrete & Continuous Dynamical Systems  A, 2014, 34 (11) : 49894995. doi: 10.3934/dcds.2014.34.4989 
[3] 
Xinfu Chen, KingYeung Lam, Yuan Lou. Dynamics of a reactiondiffusionadvection model for two competing species. Discrete & Continuous Dynamical Systems  A, 2012, 32 (11) : 38413859. doi: 10.3934/dcds.2012.32.3841 
[4] 
Gang Huang, Yasuhiro Takeuchi, Rinko Miyazaki. Stability conditions for a class of delay differential equations in single species population dynamics. Discrete & Continuous Dynamical Systems  B, 2012, 17 (7) : 24512464. doi: 10.3934/dcdsb.2012.17.2451 
[5] 
KuangHui Lin, Yuan Lou, ChihWen Shih, TzeHung Tsai. Global dynamics for twospecies competition in patchy environment. Mathematical Biosciences & Engineering, 2014, 11 (4) : 947970. doi: 10.3934/mbe.2014.11.947 
[6] 
Casimir EmakoKazianou, Jie Liao, Nicolas Vauchelet. Synchronising and nonsynchronising dynamics for a twospecies aggregation model. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 21212146. doi: 10.3934/dcdsb.2017088 
[7] 
Huanhuan Qiu, Shangjiang Guo. Global existence and stability in a twospecies chemotaxis system. Discrete & Continuous Dynamical Systems  B, 2019, 24 (4) : 15691587. doi: 10.3934/dcdsb.2018220 
[8] 
Xinyu Tu, Chunlai Mu, Pan Zheng, Ke Lin. Global dynamics in a twospecies chemotaxiscompetition system with two signals. Discrete & Continuous Dynamical Systems  A, 2018, 38 (7) : 36173636. doi: 10.3934/dcds.2018156 
[9] 
Tobias Black. Global existence and asymptotic stability in a competitive twospecies chemotaxis system with two signals. Discrete & Continuous Dynamical Systems  B, 2017, 22 (4) : 12531272. doi: 10.3934/dcdsb.2017061 
[10] 
Guangrui Li, Ming Mei, Yau Shu Wong. Nonlinear stability of traveling wavefronts in an agestructured reactiondiffusion population model. Mathematical Biosciences & Engineering, 2008, 5 (1) : 85100. doi: 10.3934/mbe.2008.5.85 
[11] 
Henri Berestycki, Luca Rossi. Reactiondiffusion equations for population dynamics with forced speed I  The case of the whole space. Discrete & Continuous Dynamical Systems  A, 2008, 21 (1) : 4167. doi: 10.3934/dcds.2008.21.41 
[12] 
Henri Berestycki, Luca Rossi. Reactiondiffusion equations for population dynamics with forced speed II  cylindricaltype domains. Discrete & Continuous Dynamical Systems  A, 2009, 25 (1) : 1961. doi: 10.3934/dcds.2009.25.19 
[13] 
Shangzhi Li, Shangjiang Guo. Dynamics of a twospecies stagestructured model incorporating statedependent maturation delays. Discrete & Continuous Dynamical Systems  B, 2017, 22 (4) : 13931423. doi: 10.3934/dcdsb.2017067 
[14] 
Tahir Bachar Issa, Rachidi Bolaji Salako. Asymptotic dynamics in a twospecies chemotaxis model with nonlocal terms. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 38393874. doi: 10.3934/dcdsb.2017193 
[15] 
Masaaki Mizukami. Boundedness and asymptotic stability in a twospecies chemotaxiscompetition model with signaldependent sensitivity. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 23012319. doi: 10.3934/dcdsb.2017097 
[16] 
Alan Mackey, Theodore Kolokolnikov, Andrea L. Bertozzi. Twospecies particle aggregation and stability of codimension one solutions. Discrete & Continuous Dynamical Systems  B, 2014, 19 (5) : 14111436. doi: 10.3934/dcdsb.2014.19.1411 
[17] 
Masaaki Mizukami. Improvement of conditions for asymptotic stability in a twospecies chemotaxiscompetition model with signaldependent sensitivity. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 269278. doi: 10.3934/dcdss.2020015 
[18] 
Alexander Kurganov, Mária LukáčováMedvidová. Numerical study of twospecies chemotaxis models. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 131152. doi: 10.3934/dcdsb.2014.19.131 
[19] 
Costică Moroşanu. Stability and errors analysis of two iterative schemes of fractional steps type associated to a nonlinear reactiondiffusion equation. Discrete & Continuous Dynamical Systems  S, 2018, 0 (0) : 121. doi: 10.3934/dcdss.2020089 
[20] 
Xie Li, Yilong Wang. Boundedness in a twospecies chemotaxis parabolic system with two chemicals. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 27172729. doi: 10.3934/dcdsb.2017132 
2018 Impact Factor: 1.313
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