Population dynamics and wave propagation in a Lotka-Volterra system with spatial diffusion

2012 ◽  
Vol 86 (5) ◽  
Author(s):  
Mao-Xiang Wang ◽  
Pik-Yin Lai
Keyword(s):  
Wave Propagation ◽  
Population Dynamics ◽  
Spatial Diffusion ◽  
Volterra System

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

scholarly journals New Conditional Symmetries and Exact Solutions of the Diffusive Two-Component Lotka–Volterra System

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1984
Author(s):  
Roman Cherniha ◽  
Vasyl’ Davydovych
Keyword(s):  
Population Dynamics ◽  
Mathematical Models ◽  
Exact Solutions ◽  
Explicit Form ◽  
Volterra System ◽  
Two Component ◽  
Nonclassical Symmetries ◽  
Enormous Number

The diffusive Lotka–Volterra system arising in an enormous number of mathematical models in biology, physics, ecology, chemistry and society is under study. New Q-conditional (nonclassical) symmetries are derived and applied to search for exact solutions in an explicit form. A family of exact solutions is examined in detail in order to provide an application for describing the competition of two species in population dynamics. The results obtained are compared with those published earlier as well.

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