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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 and Continuous Dynamical Systems  B, 2019, 24 (2) : 801829. doi: 10.3934/dcdsb.2018208 
[2] 
Bo Duan, Zhengce Zhang. A reactiondiffusionadvection twospecies competition system with a free boundary in heterogeneous environment. Discrete and Continuous Dynamical Systems  B, 2022, 27 (2) : 837861. doi: 10.3934/dcdsb.2021067 
[3] 
Xinfu Chen, KingYeung Lam, Yuan Lou. Corrigendum: Dynamics of a reactiondiffusionadvection model for two competing species. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 49894995. doi: 10.3934/dcds.2014.34.4989 
[4] 
Xinfu Chen, KingYeung Lam, Yuan Lou. Dynamics of a reactiondiffusionadvection model for two competing species. Discrete and Continuous Dynamical Systems, 2012, 32 (11) : 38413859. doi: 10.3934/dcds.2012.32.3841 
[5] 
Gang Huang, Yasuhiro Takeuchi, Rinko Miyazaki. Stability conditions for a class of delay differential equations in single species population dynamics. Discrete and Continuous Dynamical Systems  B, 2012, 17 (7) : 24512464. doi: 10.3934/dcdsb.2012.17.2451 
[6] 
Xu Pan, Liangchen Wang. Boundedness and asymptotic stability in a quasilinear twospecies chemotaxis system with nonlinear signal production. Communications on Pure and Applied Analysis, 2021, 20 (6) : 22112236. doi: 10.3934/cpaa.2021064 
[7] 
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 
[8] 
Casimir EmakoKazianou, Jie Liao, Nicolas Vauchelet. Synchronising and nonsynchronising dynamics for a twospecies aggregation model. Discrete and Continuous Dynamical Systems  B, 2017, 22 (6) : 21212146. doi: 10.3934/dcdsb.2017088 
[9] 
Huanhuan Qiu, Shangjiang Guo. Global existence and stability in a twospecies chemotaxis system. Discrete and Continuous Dynamical Systems  B, 2019, 24 (4) : 15691587. doi: 10.3934/dcdsb.2018220 
[10] 
Li Ma, Shangjiang Guo. Bifurcation and stability of a twospecies diffusive LotkaVolterra model. Communications on Pure and Applied Analysis, 2020, 19 (3) : 12051232. doi: 10.3934/cpaa.2020056 
[11] 
Anouar El Harrak, Hatim Tayeq, Amal Bergam. A posteriori error estimates for a finite volume scheme applied to a nonlinear reactiondiffusion equation in population dynamics. Discrete and Continuous Dynamical Systems  S, 2021, 14 (7) : 21832197. doi: 10.3934/dcdss.2021062 
[12] 
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 
[13] 
Xinyu Tu, Chunlai Mu, Pan Zheng, Ke Lin. Global dynamics in a twospecies chemotaxiscompetition system with two signals. Discrete and Continuous Dynamical Systems, 2018, 38 (7) : 36173636. doi: 10.3934/dcds.2018156 
[14] 
Rong Zhang, Liangchen Wang. Global dynamics in a competitive twospecies and twostimuli chemotaxis system with chemical signalling loop. Electronic Research Archive, 2021, 29 (6) : 42974314. doi: 10.3934/era.2021086 
[15] 
Tobias Black. Global existence and asymptotic stability in a competitive twospecies chemotaxis system with two signals. Discrete and Continuous Dynamical Systems  B, 2017, 22 (4) : 12531272. doi: 10.3934/dcdsb.2017061 
[16] 
Henri Berestycki, Luca Rossi. Reactiondiffusion equations for population dynamics with forced speed I  The case of the whole space. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 4167. doi: 10.3934/dcds.2008.21.41 
[17] 
Henri Berestycki, Luca Rossi. Reactiondiffusion equations for population dynamics with forced speed II  cylindricaltype domains. Discrete and Continuous Dynamical Systems, 2009, 25 (1) : 1961. doi: 10.3934/dcds.2009.25.19 
[18] 
Shangzhi Li, Shangjiang Guo. Dynamics of a twospecies stagestructured model incorporating statedependent maturation delays. Discrete and Continuous Dynamical Systems  B, 2017, 22 (4) : 13931423. doi: 10.3934/dcdsb.2017067 
[19] 
Tahir Bachar Issa, Rachidi Bolaji Salako. Asymptotic dynamics in a twospecies chemotaxis model with nonlocal terms. Discrete and Continuous Dynamical Systems  B, 2017, 22 (10) : 38393874. doi: 10.3934/dcdsb.2017193 
[20] 
Masaaki Mizukami. Boundedness and asymptotic stability in a twospecies chemotaxiscompetition model with signaldependent sensitivity. Discrete and Continuous Dynamical Systems  B, 2017, 22 (6) : 23012319. doi: 10.3934/dcdsb.2017097 
2018 Impact Factor: 1.313
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