Population Dynamics And Wave Propagation In Biological Species

Biological species is often defined as a group of organisms living and proliferating with time and space.During the temporal and spatial evolution of biological species,the interaction between the organism and organism,and the interaction between the environment and organism will constitute a unified organic whole.So the species has the property of birth rate,death rate and change in population.When these properties are quantified we can study the evolution dynamics and give some prediction through building effective mathematical models.There is a vast number of phenomena in biology seem to be the appearance of a travelling wave.?n this thesis we will focus on the population dynamics and wave propagation in biological species.Based on the traditional model on the evolution of biological species,considering the movement induced by diffusion,the reaction-diffusion partial differential equation can be written,through nonlinear dynamical analysis and direct numerical solution we can study the evolution wave and wave speed.The wave speed is determined by the proliferation and diffusion equally.When the wave speed of one species increase to critical value,the wave fronts of both species will have a change and a discontinuity in wave speed will emerge.There are six different interspecific relationships described by the LV model.First of all,we focus on the stability of the model,finding that three regions allow for stable species coexistence,namely,weak competition,mutualism,and predator-prey scenarios can lead to win-win coexistence situations.Besides,we study a self-regulating species,whose interactions can change with the other's population size.With self-regulation the interactions between two species can be changed into more stable situation and meanwhile increase the members of the final winner.From the point view of promoting diversities of species it hints that self-regulation may be better than monotonic interaction.Finally,we also studied Holling ? predator-prey model in terms of the properties of oscillation and the difference between Holling types ? and ?.