Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses

Шаповалов, А. В.

doi:10.1007/s11182-018-1236-6

Cited by 2 publications

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References 9 publications

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“…This theme has traditionally been addressed from the establishment of conservation equations that take into account the factors that affect the size of the population studied. Thus we arrive at the reaction-diffusion equations (RDE), which describe the temporal evolution of the population density

in the form [3]

These equations frequently appear in the study of systems of the most diverse nature [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , leading to interesting phenomena, such as critical behavior, multiple stationary states, spatial patterns, wave fronts and oscillations. Here Γ is the source term, whose specific form will depend on the problem under study.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Aranda

Penna

Oliveira

2021

Communications in Nonlinear Science and Numerical Simulation

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Highlights It is proposed a model based on non-local operators capable of reproduce several of the equations traditionally used in research on population dynamics, as well as having additional features, useful for describing the phenomenon of pattern formation. The combination of two of the parameters present in the model, namely, α and β , determines the existence of a phase space, characterized by regions with and without patterns. The patterns formed will have M peaks and M valleys, with M ≥ 2. There are ( α, β ) combinations which lead to the formation of degenerate states, where the system seems not to forget its initial conditions. The model allows the study of real systems, such is the case of bacterial populations subjected to inhomogeneous growth conditions. The parameter β represents a macroscopic measure of changes that occur at an individual level in the concentrations of proteins in bacteria, as a product of significant variations in the environment.

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in the form [3]

Section: Introductionmentioning

confidence: 99%

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Aranda

Penna

Oliveira

2021

Communications in Nonlinear Science and Numerical Simulation

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Analytical and Numerical Solutions of the Riccati Equation Using the Method of Variation of Parameters. Application to Population Dynamics

Aranda

Oliveira

2020

Journal of Computational and Nonlinear Dynamics

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This work presents new approximate analytical solutions for the Riccati equation (RE) resulting from the application of the method of variation of parameters. The original equation is solved using another RE explicitly dependent on the independent variable. The solutions obtained are easy to implement and highly applicable, which is confirmed by solving several examples corresponding to REs whose solution is known, as well as optimizing the method to determine the density of the members that make up a population. In this way, new perspectives are open in the study of the phenomenon of pattern formation.

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Approximate Solutions of the One-Dimensional Fisher–Kolmogorov–Petrovskii– Piskunov Equation with Quasilocal Competitive Losses

Cited by 2 publications

References 9 publications

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Analytical and Numerical Solutions of the Riccati Equation Using the Method of Variation of Parameters. Application to Population Dynamics

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