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14 p, 1.1 MB |
Planar Kolmogorov systems with infinitely many singular points at infinity
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Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Otero-Espinar, M. Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. [...]
2022 - 10.1142/S0218127422500651
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 32, Issue 5 (April 2022) , art. 2250065
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38 p, 850.7 KB |
Phase portraits of a family of Kolmogorov systems depending on six parameters
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Diz-Pita, Érika (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización) ;
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Otero Espinar, Maria Victoria (Universidade de Santiago de Compostela. Departamento de Estatística, Análise Matemática e Optimización)
We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ R provide Kolmogorov systems. [...]
2021
Electronic journal of differential equations, Vol. 2021, Issue 35 (2021) , p. 1-38
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13 p, 4.1 MB |
Global dynamics of a Lotka-Volterra system in ℝ³
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Martínez, Y. Paulina (Centre de Recerca Matemàtica) ;
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica (Portugal))
In this work we consider the Lotka-Volterra system in R³ x˙ = −x(x − y − z), y˙ = −y(−x + y − z), z˙ = −z(−x − y + z), introduced recently in [7], and studied also in [8] and [14]. [...]
2020 - 10.1080/14029251.2020.1757240
Journal of Nonlinear Mathematical Physics, Vol. 27, Issue 3 (May 2020) , p. 509-519
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13 p, 380.0 KB |
Dynamics of some three-dimensional Lotka-Volterra systems
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Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ;
Zhang, Xiang (Shanghai Jiao Tong University. School of Mathematical Sciences)
We characterize the dynamics of the following two Lotka-Volterra differential systems: ̇x=x(r+ay+bz), ̇x=x(r+ax+by+cz), ̇y=y(r−ax+cz),and ̇y=y(r+ax+dy+ez), ̇z=z(r−bx−cy), ̇z=z(r+ax+dy+fz). [...]
2017 - 10.1007/s00009-017-0927-5
Mediterranean Journal of Mathematics, Vol. 14, Issue 3 (June 2017) , art. 126
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17 p, 1.1 MB |
Hybrid approaches for multiple-species stochastic reaction-diffusion models
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Spill, Fabian (Boston University. Department of Mechanical Engineering) ;
Guerrero, Pilar (University College London. Department of Mathematics) ;
Alarcón Cor, Tomás (Centre de Recerca Matemàtica) ;
Maini, Philip K. (University of Oxford. Wolfson Centre for Mathematical Biology) ;
Byrne, Helen (University of Oxford. Wolfson Centre for Mathematical Biology)
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. [...]
2015 - 10.1016/j.jcp.2015.07.002
Journal of computational physics, Vol. 299 (Oct. 2015) , p. 429-445
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